CPM Homework Help : APCALC Problem 10-120

CPM Homework Banner

Home > APCALC > Chapter 10 > Lesson 10.2.2 > Problem 10-120

10-120.

Determine if each of the following series converges or diverges. State the tests you used.

$\displaystyle \sum _ { n = 1 } ^ { \infty } n ( \frac { 2 } { 3 } ) ^ { n }$
Hint (a):
The Ratio Test can be used.

$\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n + \sqrt { n } }$
Hint (b):
$n+\sqrt{n}\le 2n$

$\displaystyle\sum _ { n = 1 } ^ { \infty } \operatorname { ln } ( \frac { n } { n + 1 } )$
Hint (c):
$\ln\Big(\frac{n}{n+1}\Big)=\ln(n)-\ln(n+1)$
More Help (c):
Write out some terms of the series. You should notice that this is a telescoping series.

$\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ( \operatorname { ln } ( n ) ) ^ { 2 } }$
Hint (d):
What is the value of the first term of the series?

© 2022 CPM Educational Program. All rights reserved.