Consider the telescoping series Σ. (Η -- (1) Let the mth partial sum Sm = m-...
Question 10 Co Consider the telescoping series LGT) (1) Let the mth partial sum Sm = (-) Give (1) S = (ii) S2 = (11) S = (iv) In terms of m, Sm (2) Compute lim, (3) Determine if the series + S 00 (-) is convergent or divergent. Give the exact sum if it is convergent. TO Lop 12pt Paragraph BIU A 2 TY BEY B
Let Consider the geometric series M-1 (-1)^-1 got7 Sm = Enci (1) Give S2 (-1)n-1 21+1 gon (2) What area and r of the this geometric series? (3) Determine algebraically (without using a calculator) if the series is convergent or divergent and why. (4) Find the sum algebraically if it is convergent.
31 Consider the geometric series 2001 (-1)-1 Let Sm = 2-1 (-1)^-1 2071 (1) Give S2 (2) What are a and r of the this geometric series? (3) Determine algebraically (without using a calculator) if the series is convergent or divergent and why. (4) Find the sum algebraically if it is convergent.
Determine whether the series is absolutely convergent, conditionally convergent or divergent. 2"m! (b) Σ(-1)". 5 • 8 • 11 •• (3η + 2) (c) Στ (1 + Ae η =1 1 (- 2)" (-1)" (e) Σ (- 1)"e" (f) Σ (g) Σ (n + 1)! η 1 η 2 mln (2017)
Find Fourier coefficients for the following function defined on x E [-π, π] Plot the original function and the first three partial sums of the Fourier series S1, S2, S3 on the same plot. Partial sum Sn is the sum of all contributions from the frequencies less than or equal to n, i.e. Sn(x) = a0+ Σ 1 (ak cos(kx) +br sin(kx)) Find Fourier coefficients for the following function defined on x E [-π, π] Plot the original function and...
6. For each given series, complete the following tasks: (i) Prove that the series converges ab- solutely; (i) Show that the series satisfies all conditions of the Alternating Series Test; (ii) Find the partial sum sy of the series, and then estimate its remainder Ra: (iv) Determine how many terms are needed to approximate the sum of the series accurate to within 0.001, and then find this approximation. (a) L (b) Σ 27! 6. For each given series, complete the...
Please write it clearly and show every step ere Cesaro Sumrnability. Given an infinite series Σ an let Sn be the sequence of partial sums and let 5 Tt A series is Cesaro-surmable if linn-troƠn exists (and is finite). and this limit is called the Cesàro sum (a) Given the series 2n-1 n' s", hnd 8m and Ơn for any 1. and find the Cesaro sum of ΣΥ_1)". (b) Find the Cesàro sum of Here you may use the fact,...
3m Given the series m=1 4M(3m +5) Σ estimate the error in using the partial sum sg by comparison with the series |- M m=94m Select one: o a. Rg < 0.0000051 b. Rg < 0.000005 C. Rg > 0.0000052 d. R8 < 2.6130051 e. Rg > 0.0000051 (n! For which positive integers k is the series n=1 (kn)! convergent? Select one: a. k< 0 b. k <-6 c. k> 1 O d. k> 0 O e. k > 6
Question 9 10 p Consider the geometric series (-1)-**. Let S = T. (-1)-**** (1) Give S (2) What area and of the this geometric series? (3) Determine algebraically (without using a calculator) if the series is convergent or divergent and why. (4) Find the sum algebraically if it is convergent. 12pt Β Ι Ν Α TV HE TE Paragraph x $
1 Find the partial sum Sy of the series Ž Give your answer to five decimal places. n=1 3+41 Select one: a. Sz= 0.21555 b. S=0.19176 C. S7= 0.18985 d. Sz= 0.18975 e. Sz= 1.60976 Σ 3m Given the series m=1 4M(3m +5) |- estimate the error in using the partial sum sg by comparison with the series Σ 1 m=94m Select one: o a. Rg < 0.0000051 b. Rg < 0.000005 C. Rg > 0.0000052 d. R8 < 2.6130051...