- #1

karush

Gold Member

MHB

- 3,269

- 5

of the series.

$$\sum_{n=1}^{\infty}\dfrac{(-1)^n x^n}{\sqrt[3]{n}}$$

(1)

$$a_n=\dfrac{(-1)^n x^n}{\sqrt[3]{n}}$$

(2)

$$\left|\dfrac{a_{a+1}}{a_n}\right|

=\left|\dfrac{(-1)^{n+1} x^{n+1}}{\sqrt[3]{n+1}}

\cdot\dfrac{\sqrt[3]{n}}{(-1)^n x^n}\right|

=-\frac{\sqrt[3]{n}x\left(n+1\right)^{\frac{2}{3}}}{n+1}$$

(3) W|A Convergence Interval is

$$-1\le \:x\le \:1$$

ok on (2) I was expecting a different result to take $\infty$ to

on (3) the example I was trying to follow was ? on how W|A got this interval