Find the interval of convergence for the given power series

Find the interval of convergence for the given power series.

∞
Ʃ ((x-6)^n)/(n(-8)^n)
n=1

The series is convergent from x = ___ to x = ___

Using the ratio test:
r = lim(n→∞) | [(x-6)^(n+1) / ((n+1) (-8)^(n+1)))] / [(x-6)^n / (n (-8)^n)] |
..= (|x - 6|/8) * lim(n→∞) n/(n+1)
..= |x - 6|/8.

So, the series converges (at least) when |x - 6|/8 < 1 ==> |x - 6| < 8.

Checking the endpoints:
x = -2 ==> Ʃ 1/n, the divergent harmonic series
x = 14 ==> Ʃ (-1)^n/n, which converges by the Alternating Series Test.

Hence, the interval of convergence is (-2, 14].

I hope this helps!