# Math Help - Power Series problem

1. ## Power Series problem

((-1)^n(x^n))/(11^n(n^2+5))

i seem to come up with the problem being convergent from -1/11 to 1/11 but it's telling me thats not right. any ideas? thanks , Drew

2. Hello, spd579!

A simple error . . . somewhere.

$\frac{(-1)^nx^n}{11^n(n^2+5)}$

Ratio Test

. . $\left|\frac{a_{n+1}}{a_n}\right| \;=\;\left|\frac{x^{n+1}}{11^{n+1}[(n+1)^2+5]}\cdot\frac{11^n(n^2+5)}{x^n}\right|$ $= \;\left|\frac{x}{11}\cdot\frac{n^2+5}{n^2 + 2n + 6}\right|$

Divide top and bottom by $n^2$ and take the limit.

. . $R \;= \;\lim_{n\to\infty}\left|\frac{x}{11}\cdot\frac{1 + \frac{5}{n^2}}{1 + \frac{2}{n} + \frac{6}{n^2}}\right| \;=\;\left|\frac{x}{11}\right|$

Since $\left|\frac{x}{11}\right| < 1$, we have: . $-11 < x < 11$