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: 8n2 + 1n + 1 an 7n2 + 9n + 9

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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: 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: bn Уп? + 6п — п,

A: Given that the sequence bn=n2+6n-n where n∈ℕ and ℕ is the set of natural numbers. We have to…

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: The limit of the sequence a, = (-1)"2 is equal to %3D Select one: True O False

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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: 6n2 – 7n An 2n2 + 9

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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

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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: 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.

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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: Suppose you want to type sequences of vowels (that is, the letters a, e, i, o and u). However, the e…

A: Given  the number of sequences of length   (i) Find (ii) Write a second-order difference equation…

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…

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Q: 2 Given the Sequence xcn) = (6-n)[Ucn)-Ucn-6)). Make a sketch of :- a) y,n)= XC4-n) b) YeCn) = X…

A: Given: The sequence is: Xn=6-nun-un-6 The sketch of the graph is such that:

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: Find a5 for the sequence with generating function (2/(1−x)^2)*(x/(1−x−x^2)

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Q: Determine whether ∞∑n=1√n / 2n2+n+5 is convergent.

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

A: We will find out the required sequence.

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

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Q: Consider the sequence (1/2+1/2+¹). lim 818 11 (+ 1/1/2+1) = -

A: To find the limit of the given sequence.

Q: Solve the recurrence defined by a for n ≥ 1. an 3(6^n)-2 3 and : 6an-1 + 5 an =

A: As per the guidelines I am answering only one question at a time. an=6an-1+5, a0=3

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.