Question

What is the radius of convergence of `sum_1^oo (x^n ) / 6^n`?

Answer 1

`6`

Explanation:

the series is `x/6+(x/6)^2+(x/6)^3+...`, which is geometric.
geometric series converge if and only if `|ratio|<1`.
the ratio is `x/6`.
the series will converge if and only if `|x/6|<1rarr|x|<6`
the radius of convergence is `6`