licite formula for the sum (assuming n is a multiple of 3)  Q= 1·1 + 2·2 + 3·3 + 1 · 4

Q: se the summation notation to rewrite the following expression (13 − 9) − (23 − 9) + (33 − 9) − (43…

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Q: Using a binomial approach, find the sum S given by n+1 S="C₁ + "+¹C₁ + "+2² C₂+...+ "*C,

A: Here we can use the following formula to find the sum nCr+nCr+1=n+1Cr+1and nC0=1

Q: Use induction to prove the summation formula п(n+ 1)(2n +1) 6 i=1 for all n E N. Hint: In inductive…

A: Use induction to.prove the following summation formula

Q: Study the problem-solving item hereunder and respond to the accompanying questions What is the last…

A: The last digit of the sum: 11+22+33+44+⋯+20012001 is to be obtained. The last digit can be obtained…

Q: 1+(-1)" m? +1 (0.1)" +1 Evaluate the sums: (a) (b) í(4 +m²)!5 m3 Ans. 2.52; 0.1948

A: (a) ∑m=051+-1mm2+1=21+0+25+0+217+0=2+0.4+0.12=2.52

Q: b) Find the sum of the following formula. Please show your work 100 E(k² + 3k+2 +1) k=1

A: A sequence is a set of numbers that has a particular order or obeys a general form. The nth term of…

Q: Consider the sum (3)2 + (8)² + (13)2 + +(15n-2)2: ... (a) Write the sum in sigma notation.

A: Consider the sum  (3)2+82+132+.....................+(15n-2)2

Q: B. Prove that for all positive integers n, 2² +5² +8² +...+(3n − 1)² = n(6n² - 3n 2 1)

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Q: Fecu F 16 4+ (5 + 8 1

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Q: Which of the following is the correct expression for the sum below? 8 2 (k – 3) k=2 Select the…

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Q: Construct a rearrangement of Σ(−1)n-1 = 1 - 2 + 1 - 1 + ... whose sum is 1.

A: In the given problem we have to rearrange the series in such a way that the sun of the series is 1.…

Q: 74 (i + 1) j=2 (i - 1)

A: The given sum,   ∑i=2741i+15-1i-15

Q: Evaluate the summation: 1(11)+2(2!)+3(3!)+...+t(t!); t=3

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Q: Find an explicit formula to calculate the sum (assuming n is a multiple of 2)  P = 1 · 1 + 2 · 2 +…

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Q: Express the following sums using sigma notation. a. 5+6+7+8+9 b. 2+4 +6+8+ 10 + 12 c. 1° + 2° + 38 +…

A: If a1, a2, ....., an,.... be the sequence of the terms then the sequence represents as the sigma…

Q: 6. Algebraically find the sum 63 – 70 + 78 – 85 + 93 – 100 + + 2268 ...

A: Given: A finite series 63-70+78-85+93-100+...+2268 It can be observed that the series is of the form…

Q: Choose all those that represent the sum 5+7+9+11+13+...+101. 101 Σκ k = 5 50 E (2K+ 1) j = 2 50 Σ…

A: We have to find the correct representation of the sum 5+7+9+11+13+⋯+101

Q: Given that 1+ 2+3+..+n = n(n+1) 2 , then the sum 50 + 51 + 52+...+ 70 =

A: Given  1+2+3+…+n=nn+12

Q: 1 1 1 :+...(Ans. 3/4) 2) Find the sum of: 1.3 2.4 3.5 1 3) Find the sum of: 1 1 + 1.3 3.5 5.7 +...…

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Q: 8] n=1 1 5n2 + 5n

A: To Find: The sum ∑n=1∞15n2+5n

Q: n(n+1) for all n EN, • Given that 1+ 2 +3+..+n = the sum 70 + 71+72 + .+ 100 = 2

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Q: sum

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Q: Prove by mathematical induction the summation 3n +7n (3i + 2) = 5+8+11+ 14+...+(3n +2) = (Write your…

A: Summation

Q: (6/4+1) + (6/4+2)+(6/4+3)..+(6/4+15) (- 1 : 1

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