(a) Starting with the geometric series X?, find the sum of the series η ΕΟ Σ ηχο – 1, 1x] <1. ΠΕ 1 (b) Find the sum of each of the following series. DO Σηχή, 1x <1 η = 1 η (i) Σ. (c) Find the sum of each of the following series. D) Σπίη – 1)x, Ix <1 ΠΕ 2 (i) Σ - η 57 ΠΕ 2 0 i) 22 = 1
5. (12 marks) Determine whether the given series is convergent, If so, find its sum. a. Σ=4 η2-1 -η 6. Σ. 52 () C. Σ=5 4η νη+100
(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).
Consider the telescoping series Σ. (Η -- (1) Let the mth partial sum Sm = m- vnts). 1 va). Give (1) S = (ii) S2 = (iii) S3 (iv) In terms of m. Sm (2) Compute limmo Sin (3) Determine if the series. The most ama vonta) is convergent or divergent. Give the exact sum if it is convergent.
Find the Maclaurin series of 2a. Σ Preview η =0
Which is series divergent? ο Σ=1 1,000,000+η 1 1 Σ=1 1.2 1 Σ En=l n2 Σ=1 an+1
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!
η2 -1 Find the sum of the series Σ1 n=1 (m2 +1)2
Find the sum of each geometric series: ΣXe) n +3 Σ-5 b) 50 n-0 n-1 Find the sum of each geometric series: ΣXe) n +3 Σ-5 b) 50 n-0 n-1
Find the sum of the finite geometric series using the formula for Sn Σ 2(105/-1 i- 1 The sum of the finite geometric series is Sn (Round to four decimal places.)