W10 Stepwise

Due date: Thursday 3/19, 11:59pm

Ratio Test and Root Test

01

01

Ratio and root tests

Apply the ratio test or the root test to determine whether each of the following series is absolutely convergent, conditionally convergent, or divergent.

(a) ${\displaystyle \sum _{k=0}^{\infty }{\left(\frac{k}{3k+1}\right)}^k}$ $$ (b) ${\displaystyle \sum _{n=1}^{\infty }{(-1)}^n\frac{e^n}{n!}}$ $$ (c) ${\displaystyle \sum _{n=1}^{\infty }\frac{1}{(2n)!}}$

Link to original

Solution

Solutions---0200-01

Power series: Radius and Interval

02

01

Power series - radius and interval

Find the radius and interval of convergence for these power series:

(a) ${\displaystyle \sum _{n=1}^{\infty }\frac{x^n}{n^2{3}^n}}$ $$ (b) ${\displaystyle \sum _{n=1}^{\infty }\frac{x^n}{n{3}^n}}$ $$ (c) ${\displaystyle \sum _{n=1}^{\infty }\frac{x^n}{3^n}}$

Link to original

Solution

Solutions---0220-01