an n: partial sum of this serie 3n + 4n + 1 Sn n3 + 8n2 +5n + 2 Then; an T1 b) lim (4 + an) n-00

Q: 4. Ifx, = 60 and x = 90, find each of the following: %3D a. (x, - 7) b. Σx-7 C. (x, + 2) d. Ex # 60…

A: Since you have asked multiple questions we answer only question number 4.

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: limn0 In(2n-3) -) is 8. n+5 Select one: 2 non of them

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Q: Find the term containing x6  in the expansion of (x+2y)10 Please break this down in steps that I…

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Q: 23

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Q: 4.[4Y²-Y) (Y-2) 5.CxX+1)(x-2)

A:

Q: Find the sum : [00 En = n=0 (-1)" πT 2r q" (2n)!

A: We have given a series ,  ∑n=0∞ (-1)n π2n9n 2n! We need to find the sum of series ,  ∑n=0∞ (-1)n…

Q: Classworc B Auguer Alge baic Exicesions 6. ALGEBRAIC EXPRESSIONS Name: Date: 7 1. Simplify 2x – 9y…

A:

Q: The value of the following summation is: Σ₁-2 Σji 3i O No solution O 6n(n+1)/2

A: ∑i=2n∑j=in3i Remember : ∑i=1ni=ii+12∑i=1ni2=ii+12i+16

Q: 4. Let n >1 be an integer. Consider the following expression 3 (3* – 212 + 2) – 2 (3* – 3k2 + 2) k=1…

A: Let's find.

Q: Liminf of the sequence is an = √2n(√2n +4 | 3 + 1/1/0 n √2n) n is a prime number n is not a prime…

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Q: Vn2 + 1 Let (bn)neN be the sequence defined by b, 2n Let e > 0. Derive a value of N (in terms of e)…

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Q: Use the difference anti-an, to show that the given sequence {a} is strictly increasing or strictly…

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Q: How and why does the first summation in this picture turn into the finall summation?

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Q: Find the limit of the sequence ´ 4n³ – 8n² – 7 1 18 – n + n4 - n=1

A: We need to find the limit of the following sequence. So,           limn→∞ 4n3-8n2-718-n+n4=limn→∞…

Q: x[n]=20"{u[n-9]-u[n-20]} h[n]=20{u[n-9]-u[n-20]} find y[n]=x[n]*h[n] using convolution summation.

A:

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: lim 7n²+n Atạo ntsinin) ● n^n! (n+2)^(n+I)! 7e-2 but how??

A: To show that, .

Q: 3. Use the binomial theorem to prove that 2n 2n |22n–2k = (2.5)2". k k=0

A:

Q: Use the difference an+1 - an to show that the given sequence {a,} is strictly increasing or strictly…

A:

Q: Find Launet series nepubatetion of 2 <ZK3 . %3D 2(2-2) (2-3)

A: To find the Laurent series representation of  fz=1zz-2z-3 in the region 2&lt;|z|&lt;3 first, we…

Q: P1. In the binomial expansion of (2-3) written in terms of descending power of X, find; a the th…

A: Explained below

Q: 2n+2. 10-"| n=1

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Q: True or False. Briefly explain why.  {−13, −6, −3, 1, 10} is a complete residue system modulo 5.

A:

Q: Consider the arithmetic sequence S, where the i-th term of S is defined as follows for positive…

A: Solution; The arithmetic sequence is defined by Si=2+6i-1 We want to prove by induction that the sum…

Q: (c) Let a1 = 1 and let a2 = T. For n > 3, we define recursively an = an-2 – an-1. Is it true that…

A: As per company guidelines we are supposed to answer one question at a time. for solution of other…

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: In binomial if g(x) =0, then

A: Given:  gxnx=0                                        (1)

Q: 3 (a) Express 3+9x (1+x)(3+5x) in the form A B 1+x+3+5x where A and B are integers.

A: Note:- These are multiple questions and according to company guideline we can do maximum 1 question…