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Problem 0.3 diverge: (1) m=0 1+n³ (2) Σ^=15"+3" (3) Σn=0 1-n+n² 1 In(n) Determine whether the following series converge c

Problem 0.3 diverge: (1) m=0 1+n³ (2) Σ^=15"+3" (3) Σn=0 1-n+n² 1 In(n) Determine whether the following series converge c

Advanced Engineering Mathematics
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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**Problem 0.3** Determine whether the following series converge or diverge: (1) \(\sum_{n=0}^{\infty} \frac{n^2}{1+n^3}\) (2) \(\sum_{n=1}^{\infty} \frac{4^n}{5^n + 3^n}\) (3) \(\sum_{n=0}^{\infty} \frac{1}{1+n+n^2}\) (4) \(\sum_{n=1}^{\infty} \frac{\ln(n)}{n}\) (5) \(\sum_{n=2}^{\infty} \frac{n^3}{(n^2-1)}\)
Transcribed Image Text:**Problem 0.3** Determine whether the following series converge or diverge: (1) \(\sum_{n=0}^{\infty} \frac{n^2}{1+n^3}\) (2) \(\sum_{n=1}^{\infty} \frac{4^n}{5^n + 3^n}\) (3) \(\sum_{n=0}^{\infty} \frac{1}{1+n+n^2}\) (4) \(\sum_{n=1}^{\infty} \frac{\ln(n)}{n}\) (5) \(\sum_{n=2}^{\infty} \frac{n^3}{(n^2-1)}\)
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