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3. Determine whether the follow series converge or diverge. If it converges, find its sum. a) Σ=13*+14-n 2" +4" b) Σπ=1 en c) E=4 (√√²+1)

3. Determine whether the follow series converge or diverge. If it converges, find its sum. a) Σ=13*+14-n 2" +4" b) Σπ=1 en c) E=4 (√√²+1)

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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Question

Determine whether the follow series converge or diverge. If it converges, find its sum.

a) ∑ ∞ 

n=1     (3^(n+1))*4^-n

b) ∑ ∞ 

n=1   2^n+4^n/e^n

c) ∑ ∞ 

n=4   (1/sqrtn-1/sqrtn+1)

**Exercise 3: Series Convergence or Divergence** Determine whether the following series converge or diverge. If it converges, find its sum. a) \(\sum_{n=1}^{\infty} 3^{n+1} 4^{-n}\) b) \(\sum_{n=1}^{\infty} \frac{2^{n+4} n^2}{e^n}\) c) \(\sum_{n=4}^{\infty} \left( \frac{1}{\sqrt{n}} - \frac{1}{\sqrt{n+1}} \right)\)
Transcribed Image Text:**Exercise 3: Series Convergence or Divergence** Determine whether the following series converge or diverge. If it converges, find its sum. a) \(\sum_{n=1}^{\infty} 3^{n+1} 4^{-n}\) b) \(\sum_{n=1}^{\infty} \frac{2^{n+4} n^2}{e^n}\) c) \(\sum_{n=4}^{\infty} \left( \frac{1}{\sqrt{n}} - \frac{1}{\sqrt{n+1}} \right)\)
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