Question

sum [k=2, inf] (1-2^(k+1)) / 3^k

Answer 1

\[\sum_{k=2}^{\infty} \frac{ 1-2^{k+1} }{ 3^{k} }\]

Answer 2

Its limit?

Answer 3

Split it into (1/3)^k - 2.(2/3)^k
Thus you'll get 2 infinite GPs.
Are you following ?

Answer 4

I'm following but how do I proceed?