Answer part D for me k(k +3)

The series is ∑k=1∞1kk+3-12k Write it as ∑k=1∞1kk+3-∑k=1∞12k Clearly, the series ∑k=1∞1kk+3≤∑k=1∞1k2…

Answered: k(k +3)

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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Answer part D for me

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Solution:

The series is $\sum_{k = 1}^{\infty} (\frac{1}{k (k + 3)} - {(\frac{1}{2})}^{k})$

Write it as $\sum_{k = 1}^{\infty} \frac{1}{k (k + 3)} - \sum_{k = 1}^{\infty} {(\frac{1}{2})}^{k}$

Clearly, the series $\sum_{k = 1}^{\infty} \frac{1}{k (k + 3)} \leq \sum_{k = 1}^{\infty} \frac{1}{k^{2}} and \sum_{k = 1}^{\infty} {(\frac{1}{2})}^{k}$ are convergent.

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