Question

The sum of the series $\frac{2}{3}+\frac{8}{9}+\frac{26}{27}+\frac{80}{81}+.........$ to n term , is -

• A. $n+\frac{1}{2}\left(3^n-1\right)$
• B. $n-\frac{1}{2}\left(3^n-1\right)$
• C. $n-\frac{1}{2}\left(3^{-n}-1\right)$
• D. $n-\frac{1}{2}\left(1-3^{-n}\right)$

Answer 1

The correct option is D $n-\frac{1}{2}\left(1-3^{-n}\right)$