∞ ■Consider the series Σ an where an = n=1 1 n(n + 3)* k (a) Find a formula for the kth partial sum, Sk = Σ a n=1 an. (b) Hence show that the series converges, and find its limit.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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(1) Consider the series Σ an where an =
n=1
1
n(n + 3)*
(a) Find a formula for the kth partial sum, sk
k
Σαπ
n=1
(b) Hence show that the series converges, and find its limit.
Transcribed Image Text:(1) Consider the series Σ an where an = n=1 1 n(n + 3)* (a) Find a formula for the kth partial sum, sk k Σαπ n=1 (b) Hence show that the series converges, and find its limit.
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