Problems

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) ${\displaystyle \sum _{n=1}^{\infty }\frac{x^n}{3^n}}$

02

Power series - radius and interval

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

(a) ${\displaystyle \sum _{n=0}^{\infty }{(-1)}^n\frac{{(x+3)}^n}{n!}}$ $$ (b) ${\displaystyle \sum _{n=1}^{\infty }{(-1)}^n\frac{{(x-7)}^n}{n}}$ $$ (c) ${\displaystyle \sum _{n=12}^{\infty }{n}^n{(x-2)}^n}$

03

Power series - radius and interval

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

(a) ${\displaystyle \sum _{n=0}^{\infty }\frac{{(x-8)}^n}{n^4+1}}$ $$ (b) ${\displaystyle \sum _{n=1}^{\infty }\frac{x^n}{3\cdot 7\cdot 11\cdots (4n-1)}}$