Question

Find the interval of convergence of the series.

Answer 1

\[\sum_{n=0}^{\infty} (\sin x/10)^n \]

Answer 2

A geometric series of the form \(\sum x^n\) converges for \(|x|<1\). This means that the given series must converge when \(\left|\dfrac{\sin x}{10}\right|<1\), or \(\left|\sin\dfrac{x}{10}\right|<1\) (not sure which one you meant to use).

Answer 3

Thank you so much for the help! :D

Answer 4

yw

Answer 5

You may be expected to leave your answer in terms of \(x\).