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(5) For n = 5, Verify the following summation formula: Σ + 1 (1) (η + 2)2"-1 10
By considering the summation: 2+22+23+…..+2n-1 A). What is the formula used for the summation? ________________________ B). Prove that your formula is correct for all integers n>=2 by mathematical induction.
5. Σ cosh -1 6. Σ n=2 logn n 7. Σ πιο +1) nlog(n+1) n=1 n=2 8.Σ (n!)?(2η)!(3n51 - 43n10)18" η" (3η)! nel
i need both the answers . please do both
1. [10 points] Summation formula. Show that n1- n+1 i-0 Hint: (1-1) Σ ri is a telescoping sum. i-0 2. [10 points] Integration by parts. Show that -Ax
3. Find a closed formula for the exponential generating function A(x) Σ an,n wh n+1-(n + 1)(m-n + 1), a,-1. ere an satisty the recursion a
3. Find a closed formula for the exponential generating function A(x) Σ an,n wh n+1-(n + 1)(m-n + 1), a,-1. ere an satisty the recursion a
5. (a).Determine the following summation. Use summation formulas and properties of summation: (* +2i+1) - 3.X +5.** +1 -2.sinx. (6) Secure two antiderivatives of Clearly label!
Q3: determine wither the following series are converge or diverge In(n? +3) n!.inn a) Σ=1 n=2 (n+3) n (n+2)! (12 point) c) Σ=2 8 b) Σ=1 3+ (3)an d) Σ-1 In(n) 3 (m)2
What is the theta of the following summation: 1^3 + 2^3 + 3^3+ ... +i^3+ ... + N^3
2. Find a formula for Σ LVk] when n is a positive integer.
2. Find a formula for Σ LVk] when n is a positive integer.
2. Test the Series for convergence or divergence. In(n) Σ(-) Σ- 4 n=3 η=1 n 3. Determine which option is absolutely converges and explain in details the reason. 1 (=Σ(-1)" 3 =Σ(-1)" C-Σ(-1)* tan(n) η Υ -Σ-1): E = None of these n!