(3) Zn = (-1)"-* +", where k is any integer. (4) Zn = n² +/n? (5) Z, = (5 – 4i)" In problems 6 - 10, determine if the given series is convergent. Use ratio test, alternating series test, etc. (6) S = E-o Hint: split the series into 2 series n2-i (7) S = E Ln=0 (3n+1) (-1)"(1+1)an (8) (n)! (9) S = En=1 Hint: split the series into 2 (or more) series (10) Given the Taylor series f(z) = a„(z – z,)" n=0 Find the Taylor series of the kth derivative (flk) (z)) in sigma notation form in terms of n, k, Z, Zg, and a, -
(3) Zn = (-1)"-* +", where k is any integer. (4) Zn = n² +/n? (5) Z, = (5 – 4i)" In problems 6 - 10, determine if the given series is convergent. Use ratio test, alternating series test, etc. (6) S = E-o Hint: split the series into 2 series n2-i (7) S = E Ln=0 (3n+1) (-1)"(1+1)an (8) (n)! (9) S = En=1 Hint: split the series into 2 (or more) series (10) Given the Taylor series f(z) = a„(z – z,)" n=0 Find the Taylor series of the kth derivative (flk) (z)) in sigma notation form in terms of n, k, Z, Zg, and a, -
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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