In this video I show that if a power series with powers 6^n is divergent by the Radius of Convergence Theorem then the series with powers 10^n is also divergent.
A power series has 3 conditions, it's either convergent at x = a = 0 in our case, or converges for all x, or converges whenever |x - a| is less than R, termed the radius of convergence.
In our case, x = 6 and a = 0, but the series diverges, so R is less than 6.
This means that R is less than 10 as well, so our given series is also divergent.