how that the sequence (1 – (-1)" +1/n) is divergen

Q: 5. What is meant by the index of a term of a sequence?

A:

Q: determine the limit of the sequence or show that the sequence diverges. an = 21/n2

A: Given that, an=21n2

Q: What is the generating function for the sequence {ck},where ck represents the number of ways to make…

A:

Q: The sequence with general term an = (-1)" is divergent. True False

A: The given sequence is divergent.

Q: What are absolute converging, conditional converging and divergent sequences ? (nln n)

A:

Q: Find the 5th term of the geometric sequence with first terma1 = 5 and common ratio r = - 2

A: A geometric sequence is a sequence where each term is found by multiplying the previous term by a…

Q: Find the 11th term of the harmonic sequence1/5,1/8/1/11,1/14,. . .

A: harmonic progression is 1arithmetic progression the given series has a pattern of = 13+previous term…

Q: Find the first five terms of the recursive sequence defined below. ti -2 %3D tn = tn-1+3 Select the…

A:

Q: Find the generating function for the finite sequence 2, 2,2, 2, 2, 2.

A: Step 1: Consider the provided question, Given, the finite sequence 2, 2, 2, 2, 2, 2.

Q: A sequence is defined by tn = tn-1 +2", and t1 = 1. Determine the fourth term in this sequence.

A:

Q: The greatest lower bound for the sequence {2, 4, 8, 16, 32, 64, . } is

A:

Q: The greatest lower bound for the sequence {0.1,0.01,0.001, 0.0001, ...} is

A:

Q: What does it mean for a sequence to be defined recursively?

A: A recursive sequence fnnadditionally known as a recurrence sequence is a sequence of numbers f(n)…

Q: Prove that the sequence is increasing.

A: In this question, we have given a sequence  an=(1+1n)n+11+1n To prove the sequence is increasing by…

Q: What are the first 5 terms of the sequence a_ =2n – a 'n - 1, where “, =5,

A:

Q: Cn = Jns -Jn? 13 ニ

A: The given sequence is an=n3-n2.

Q: The first five terms of the sequence tn = 1(1/3)n-1 are: If necessary, express terms as improper…

A: We can find the required terms as below.

Q: Find the limit of the sequence 14n2 – 8n – 7 1 18 – n + 7n² . - - - n=1

A:

Q: 7. What is the 10th term of the sequence defined by a, = 5p³q² and an = O an-1?

A:

Q: 3) Justify whether the sequence converges diverges or a-an. 2-n こうe abicai b- an =(-1)"

A: Given: a. an=n2e-n, b. an=-1nn2+1n2+3

Q: A sequence is defined by tn = tn-1+2", and t1 = 1. Determine the fourth term in this sequence.

A:

Q: 17th term of the sequence 7,4, 1,......

A: For part (1) We have to find out the 17th term of the given sequence.

Q: What are the first five terms of the sequence defined over the natural numbers with the explicit…

A:

Q: The generating function of the sequence 4,4,4,4,4 is

A: # To find generating function of sequence  4,4,4,4,4,4 ??

Q: Which sequence could be described by the first term: Aj = 1 and the recursive (an)² + 1 definition:…

A: Given, an+1=an2+1 a1=1

Q: Find the 10th term of the geometric sequence. aj1 = -5, r = - %3D %3D 10th term:

A: →nth term any geometric sequence is given by,                            an = a1 rn-1 , Where a1  is…

Q: It is a sequence where every term after the first is obtained by multiplying a non-zero constant. O…

A: To tell which is the sequence where every term after the first is obtained by multiplying a non-zero…

Q: A sequence is defined by tn=tn−1+3n and t1=1 Determine the fourth term in this sequence

A:

Q: A sequence that does not have any convergent subsequence

A: We find a sequence that does not have any convergent subsequence.

Q: Determine the sum of the first 6 terms of the geometric sequence. 1,2, 4, .. So

A: A geometric progression is a type of sequenc in which ratio of two consecutive terms is always a…

Q: Supposed vn =17-n2  is the explicit specification for a sequence. How many values of n (positive)…

A: Given: Vn=17-n2

Q: What is a recursively defined sequence?

A:

Q: Find ai for the sequence with generating function, 1-x 1 x x

A: Simplify the generating function.

Q: 7. Provide an example of a monotonic decreasing sequence that converges to 1.

A:

Q: Create your own sequence with recursive formula.

A:

Q: Is the sequence an=n3/3n-1 convergent or divergent? explain.

A: The given sequence is: A sequence an is said to be convergent if, where "l" is a finite number.…

Q: Find the sequence corresponding to generating function 1/(1-az).

A: We will find out the required sequence.

Q: Show that (1/n²+ n+1)!nEN is a Cauchy sequence.

A: Solution :-    The given sequence is              an =   1/( n2 + n + 1 )     ;  n belong to N .…

Q: Show that the sequence {1, -1, 1, -1, 1, -1, ..., (-1)n+1, ...} diverges.

A:

Q: Discuss the non decreasing and Bounded of the sequence 5,5,5,5,5

A:

Q: 3. Show that the sequence an = 1+ is a Cauchy sequence. Hint: Every convergent sequence is a Cauchy…

A: Cauchy sequence and it's convergence

Q: 4. Let (bn) be a sequence defined by 4bn-2 - bn-1 n > 2 b, n = 1 -1 n = 0

A:

Q: Determine whether the real sequence of convergent or divergent sequence. n+3 converges by using the…

A: This is a problem of sequence.

Q: The twentieth term of sequence an = %3D 11+1

A: Here is the solution:

Q: Find the infinite sum of the geometric sequence with a = 6, r = if it exists. %3D %3D

A:

Q: How can you know if a sequence diverges or converges?

A: Answer :  We can know that a sequence is  diverges or converges ,  We have to remember that of a…

Q: The sequence (a,) = 2 converges to -2.

A: Let (an) be a sequence. If limn→∞an = L, where L is finite Then the sequence converges, otherwise it…

Q: Find a closed form for the generating function for this sequence.   1, 0, 1, 0, 1, 0, 1, 0, ...

A: We have to find a closed form for the generating function for this sequence.   1, 0, 1, 0, 1, 0, 1,…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.