The two convergent subsequences of the sequence (-1)™+2 is a) x, = (-1)" +2 and x, = +2 %3D 2n+1 6n b) X2, =(-1)" +2 and x,1 =(-1)' +2 3n 2n+1 c) x, = (-1)" +2 and x,1 = (-1)** +2 3n d) x, =(-1)"+2 and x,-1 =(-1)" +2 %3D

Q: Find the sum of the first 6 terms of the sequence defined by an = -4 (2)^-¹ for n ≥ 1. -

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Q: The simple formula for a, if the first 5 terms of the sequence {an} are 1, 21, 121, 621, 3121 is:…

A: We are asked to find which is correct for the sequence.

Q: limit of this sequence

A: We have to find out the limit of the given sequence.

Q: Find lim,00 sup(sn) and lim,→0 inf(sn) for the sequence: 82n = (-1)"(n); s2n-1= e7 = et

A: The sequence is S2n=-1nn. Find limn→∞sups2n and limn→∞infs2n: Consider and obtain the limits:…

Q: Find the limit of the sequence: 3n² + 3n+6 ап 7n² + 7n +9

A: Step 1: The limit of a sequence is the value that the terms of the sequence approach as the index n…

Q: Which of the following is the generating function for the sequence 5, 5, 5, 5 O A. G(x)=(1-x) 1 O B.…

A: Generating Function: Generating Function is a way to represent an infinite sequence. Consider a…

Q: Q5 (a) Find the area of the region enclosed by the lines and curves, y=x' -2,and y =2

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: a,=(- 1)" is a divergent sequence

A:

Q: 4. Consider the sequence 8 1 {2(k+3 (2(k+3)) k=1 rewrite the sequence from j-5

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Q: The number sequence a1, a2, a3, .... is defined by a1 = 8 a2 = 24 and recursion formula 4an + 1…

A: We need to show that an=5n-12n-2 for a1=8 and a2=24  The given recursion formula is…

Q: What is the summation from n = 1 to infinity, of  (3n+1) / (5n + 4) ?

A:

Q: Find the explicit formula for the geometric sequence b, with the following information given. bị = 7…

A: Given : b1=7b4=-5627

Q: Sequence hWith frst tem 7, and las term 7/729.

A:

Q: 5. (i) Determine the sequence gnerated by the following generating functions: (ii) e(1+x) t (1-1)³

A: (5) (i)          Given generating function is t1-t3= t 1-t-3…

Q: 3 Find (- 3)'-1 i=1

A: Given : ∑i=13-3i-1

Q: an = (-1)", bn Cn = n² dn= n (a) For each sequence, give an example of a monotone subsequence. 6n +…

A:

Q: f(n)=(n-1/2) (n-1/3) Its n-1 over 2 and n-2 over 3 Write the first six terms of the sequence…

A:

Q: The partial sum-2 + (-8) + (-32)+...+(-32768) equals

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Q: Suppose ao, a1, a2,... is a sequence such that ao = a1 = 1 and forn2 1, an+1 = n(an+an-1). Find az =…

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

A: Simplify the generating function.

Q: In step 3, how does (x+1)x! become (x+1)! in the denominator of the summation?

A: x!=x(x−1)(x−2)..........(2)(1)..................formula…

Q: a. the sequence is given by an=1/(n^7/6)      lim n→∞ an=  b.  the sequence is given by…

A: We need to solve separately a. the sequence is given by an=1/(n^7/6)      lim n→∞ an=  b.  the…

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

A: We will find out the required sequence.

Q: 2.1. Write the first five terms of each of the following sequences. 2n -1 (a) 3n + 2 1-(-1)" (b)…

A: Given: Five sequences. Substitute n=1, 2, 3, 4, 5 to find the first five sequences in the given…

Q: E. In a sequence: а1 3 3, ад — 7, and a, — 2ад-1 + аm-2 for n > 3. (12) Find a3. (13) Find a4.

A: Given,  a1=3, a2=7, an=2an-1+an-2

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.