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What is the radius of convergence of $\infty \sum 1 \frac{x^{n}}{6^{n}}$ $sum_1^oo (x^n ) / 6^n$ ?

1 Answer

May 25, 2018

$6$ $6$

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 $6$

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