## Multivariable Calculus, 7th Edition

Published by Brooks Cole

# Chapter 11 - Infinite Sequences and Series - 11.2 Exercises - Page 735: 7

#### Answer

The series is divergent

#### Work Step by Step

$\Sigma^{\infty}_{n=1} \frac{n}{1+\sqrt n}$ $a_{n}= \frac{n}{1+\sqrt n}$ partial sum $s_{n} = a_{1} + a_{2} +... a_{n}$ $n=1$ $a_{1}=0.500$ $s_{1}=0.500$ $n=2$ $a_{2}=0.82843$ $s_{2}=1.3284$ $n=3$ $a_{3}=1.09808$ $s_{3}=2.4265$ $n=4$ $a_{4}=1.3333$ $s_{4}=3.7598$ $n=5$ $a_{5}=1.54508$ $s_{5}=5.3049$ $n=6$ $a_{6}=1.73939$ $s_{6}=7.0443$ $n=7$ $a_{7}=1.92004$ $s_{7}=8.9644$ $n=8$ $a_{8}=2.08963$ $s_{8}=11.0540$ The partial sum appears to be increasing without bound so the series is divergent.

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