Question

how to i find the series' radius and interval of converges

Answer 1

use the ratio test or the root test
given \[\large \sum_{n=0}^{+\infty}a_nx^n\] solve the inequality \[\large \lim_{n \rightarrow +\infty} \left| \frac{ a_{n+1} x^n}{ a_n x^n } \right|<1\] or \[\large \lim_{n \rightarrow +\infty} \sqrt[n]{a_n x^n}<1\] by evaluating the limit at the LHS and solving the inequality in |x|

Answer 2

so what would the solution for this be?