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)

Math

Advanced Math

k(k +3)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.3: Systems Of Inequalities

Problem 7E

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Question

Answer part D for me

Expert Solution

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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