Problem 1E: Each of Exercises 16 gives a formula for the nth term an= of a sequence {an}. Find the values of a1,... Problem 2E: Each of Exercises 1–6 gives a formula for the nth term an of a sequence {an}. Find the values of a1... Problem 3E: Each of Exercises 16 gives a formula for the nth term anof a sequence {an}. Find the values of a1a2,... Problem 4E: Each of Exercises 1–6 gives a formula for the nth term an of a sequence {an}. Find the values of a1,... Problem 5E: Each of Exercises 1–6 gives a formula for the nth term an of a sequence {an}. Find the values of a1... Problem 6E: Each of Exercises 1–6 gives a formula for the nth term an of a sequence {an}. Find the values of a1,... Problem 7E: Each of Exercises 7–12 gives the first term or two of a sequence along with a recursion formula for... Problem 8E: Each of Exercises 7–12 gives the first term or two of a sequence along with a recursion formula for... Problem 9E: Each of Exercises 7–12 gives the first term or two of a sequence along with a recursion formula for... Problem 10E: Each of Exercises 7–12 gives the first term or two of a sequence along with a recursion formula for... Problem 11E: Each of Exercises 7–12 gives the first term or two of a sequence along with a recursion formula for... Problem 12E: Each of Exercises 7–12 gives the first term or two of a sequence along with a recursion formula for... Problem 13E: In Exercises 13–30, find a formula for the nth term of the sequence.
13. 1, −1, 1, −1, 1, ...
l’s... Problem 14E: In Exercises 13–30, find a formula for the nth term of the sequence.
14. −1, 1, −1, 1, −1, ...
l’s... Problem 15E: In Exercises 13–30, find a formula for the nth term of the sequence.
15. 1, −4, 9, −16, 25,... Problem 16E: In Exercises 13–30, find a formula for the nth term of the sequence.
16.
Reciprocals of squares of... Problem 17E: In Exercises 13–30, find a formula for the nth term of the sequence.
17.
powers of 2 divided by... Problem 18E: In Exercises 13–30, find a formula for the nth term of the sequence.
18.
Integers differing by 2... Problem 19E: In Exercises 13–30, find a formula for the nth term of the sequence.
19. 0, 3, 8, 15, 24,... Problem 20E: In Exercises 13–30, find a formula for the nth term of the sequence.
20. −3, −2, −1, 0, 1,... Problem 21E: In Exercises 13–30, find a formula for the nth term of the sequence.
21. 1, 5, 9, 13, 17, ...
Every... Problem 22E: In Exercises 13–30, find a formula for the nth term of the sequence.
22. 2, 6, 10, 14, 18, ...
Every... Problem 23E: In Exercises 13–30, find a formula for the nth term of the sequence.
23.
Integers differing by 3... Problem 24E: In Exercises 13–30, find a formula for the nth term of the sequence.
24.
Cubes of positive integers... Problem 25E: In Exercises 13–30, find a formula for the nth term of the sequence.
25. 1, 0, 1, 0, 1,... Problem 26E: In Exercises 13–30, find a formula for the nth term of the sequence.
26. 0, 1, 1, 2, 2, 3, 3, 4,... Problem 27E Problem 28E Problem 29E: In Exercises 13–30, find a formula for the nth term of the sequence.
29.
Problem 30E: In Exercises 13–30, find a formula for the nth term of the sequence.
30.
Problem 31E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 32E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 33E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge'? Find the limit of each... Problem 34E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 35E: Which of the sequences {an} in Exercises 31100 converge, and which diverge? Find the limit of each... Problem 36E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 37E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 38E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 39E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 40E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 41E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 42E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 43E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 44E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 45E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 46E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 47E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 48E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 49E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 50E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 51E: Which of the sequences {an} in Exercises 31–100 converge and which diverge? Find the limit of each... Problem 52E: Which of the sequences {an} in Exercises 31–100 converge and which diverge? Find the limit of each... Problem 53E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 54E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 55E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 56E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 57E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 58E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 59E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 60E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 61E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 62E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 63E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 64E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 65E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 66E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 67E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 68E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 69E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 70E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 71E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 72E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 73E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 74E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 75E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 76E: Which of the sequences {an} in Exercises 31−100 converge, and which diverge? Find the limit of each... Problem 77E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 78E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 79E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 80E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 81E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 82E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 83E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 84E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 85E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 86E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 87E: Which of the sequences {an} in Exercises 31–100 converge, and which diverge? Find the limit of each... Problem 88E Problem 89E Problem 90E Problem 91E Problem 92E Problem 93E Problem 94E Problem 95E Problem 96E Problem 97E Problem 98E Problem 99E Problem 100E Problem 101E: In Exercises 101–108, assume that each sequence converges and find its limit.
101. a1 = 2,
Problem 102E: In Exercises 101–108, assume that each sequence converges and find its limit.
102. a1 = −1,
Problem 103E: In Exercises 101–108, assume that each sequence converges and find its limit.
103. a1 = −4,
Problem 104E: In Exercises 101–108, assume that each sequence converges and find its limit.
104. a1 = 0,
Problem 105E Problem 106E Problem 107E: In Exercises 101–108, assume that each sequence converges and find its limit.
107.
Problem 108E: In Exercises 101–108, assume that each sequence converges and find its limit.
108.
Problem 109E Problem 110E Problem 111E Problem 112E Problem 113E Problem 114E Problem 115E Problem 116E Problem 117E Problem 118E Problem 119E Problem 120E: Prove Theorem 3.
THEOREM 3–The Continuous Function Theorem for Sequences
Let {an} be a sequences of... Problem 121E: In Exercises 121–124, determine whether the sequence is monotonic and whether it is bounded.
121.
Problem 122E Problem 123E Problem 124E Problem 125E: In Exercises 125–134, determine whether the sequence is monotonic, whether it is bounded, and... Problem 126E: In Exercises 125–134, determine whether the sequence is monotonic, whether it is bounded, and... Problem 127E: In Exercises 125–134, determine whether the sequence is monotonic, whether it is bounded, and... Problem 128E: In Exercises 125–134, determine whether the sequence is monotonic, whether it is bounded, and... Problem 129E: In Exercises 125–134, determine whether the sequence is monotonic, whether it is bounded, and... Problem 130E Problem 131E Problem 132E Problem 133E Problem 134E Problem 135E Problem 136E Problem 137E Problem 138E Problem 139E Problem 140E Problem 141E Problem 142E Problem 143E Problem 144E Problem 145E Problem 146E Problem 147E Problem 148E Problem 149E Problem 150E Problem 151E Problem 152E Problem 153E Problem 154E Problem 155E Problem 156E Problem 157E Problem 158E format_list_bulleted