convergence. n=0 (n+1)3 00 n+1 x2+1 n=0(n+1)3 (+1) x^2+1 n=0(n+1)3" 00 1n (3) - Σ In (3) - (n+1) 00 X n n=1 n3 72 72 n=1n3n " " " R = 1 R = 1 R=3 R = 3 R = 1

Q: Prove n (1+x)n-1= Σ c(n, k) k xk-1. k=1

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Q: 4. Find the power series representation of the form Σ=o arn where f(x) 7 2 + x f(x) = a) Σ n=0 7·χη…

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A: Both series we can evaluate using geometric series method.

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A: Given that ; U follows binomial distribution.  We want to find P( U> 1) =?  So by using binomial…

Q: 11. Find the Maclaurin series for | cos (2x³) dx. OS

A: here we have to find the intregration

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A: Dear student. You have posted many questions. In our policy, i have answering the first question. If…

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Q: 8. Give a closed form for the sum You may assume that Σk=1 k = n(n+1) 2 1x2+2x3+ ... k(k + 1) and…

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Q: 9) Σ=1 10) 3/3 - (-1)^(1+n²) n! 3 1 4 2 11) Σ.» (= − 1) =0 τη 13) Σ=1 14) En=1 15) En=1 Σ + n+1 12)…

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A: We have to prove given identity:

Q: 2n2 + n8 1. 935n10 + 7n² + 6 9n5 + n² – 9n 2. 7n13 6n10 + 5 бп? + 9n7 3. 2n8 + 7n³ – 2 n=1

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Q: (a) > [Integral Test] n2 + 108 n=1 1 ( b) Σ (2n + 3)17 [Comparison Test] n=1

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Q: If f(n) (0) (n + 1)! for n = 0, 1, 2, 00 n = 0 00 = (n + 1)x" Σ (-1) + 1, (-1)+1x n = 0 00 Σn! -x" n…

A: Step 1:Step 2:Option A is true.And radius of convergence is 1.

Q: 3. (a) Discuss convergence of the sequence {n} defined by the recurrence relation ₁ = 2 and n+1 = (n…

A: We have to discuss the convergence of the sequence xn defined by the recurrence relation x1=2 and…

Q: 2. Prove that |µ(n)| _ S(s) S(2s) n=1 if s > 1.

A: Riemann zeta function is a complex-valued function defined as ςs=∑n=1∞1ns.  There is a relationship…

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Q: 1. Determine the limits of the sequences (an), (bn),(Cn) and (dn), where 6n2 – 7n An b, = Vn² + 6n –…

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A: Mathematical Induction is a mathematical technique which is used to prove a statement is true for…

Q: L{(1+t")e*3t}=

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Q: L{(1+t")e 3t)= (1+)() n! sn+1 -3 1 n! s-3 sn+1 1 n! s+3 (s+3)"+1 n! 1+ sn+1 )() (2) s+3 (1)

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Q: Discuss the Convergence or Divergence for D { [4+ (-0"]" (Z+2)" こう 2n+1 - DZ² 2 لع Wi ngo (2n+¹)!

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Q: 13. (a) Express each of following sum in sigma notation 1 a) 1 + 2 + 113 +... + 1 20 b)…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: "Calculate the exact value of the sum using the binomial theorems 8 = Σ ([8], [n])( - 1)” 3″ - 8 3¹…

A: To calculate the exact value of the sum by using the binomial theorem.

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Q: 1.Which of the following recurrence relation should be obtained when power series solution method is…

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Q: 1 Find L-! 2(s – 1)

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Q: Question 1.3. (1) Show that 6 divides 7" +n³-3n² + 2n-1. for all integers n ≥ 0. C

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