Use the Limit Comparison Test to determine whether the series converges or diverges:
sum from n=1 to infinity of 1/(6^n - 3^n)
Identify b_n in the following limit:
lim n to infinity (a_n / b_n) = lim n to infinity (1/(6^n - 3^n)) / (1/6^n) = L
Since L is a finite number, L > 0, and b_n is convergent, the series is convergent.