(5) For n = 5, Verify the following summation formula: Σ + 1 (1) (η +...
(6) For n=3, Verify the following summation formula: Σ (1) 2' 3.
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!
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
We have a dataset with n = 10 pairs of observations (li, yi), and η Σ α: = 683, Σμι = 813, i=1 η i=1 η Σ? = 47, 405, Σαιξε = 56, 089, Συ - Συ? = 66, 731. i=1 What is an approximate 99% confidence interval for the mean response at xo = 90?
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
(1) Determine whether the following series converge or diverge: (a) Σ=0 η2 n=1 (b) Σ=0 520 και (c) Σ=2 /n ln (η) 2n (4) Σ. sin(1) η2 (e) Σ1 (1) Σ=1 n2-3n+1 ln(η).
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.
Exercise 1 (pts 5). Prove that Σσι(α) = ” + Οζω log(n). . - Τ. η<α π2 We recall that Σ
2-15 Determine whether the series is convergent or divergent. 1 2. Σ 1.0001 3. Σ 1-0.00 n=5 η n=1 σο 2 3 4. Σ 5. Σ (1) ده است + ηψη 3 n=1 1 1 6. Σ 7. Σ η=5 (η – 4)? 2n + 3 n=1
Σ(6-3-1) η-1