Question

The sum of the series n terms of the series $3+\frac{5}{2}+\frac{9}{4}+\frac{17}{8}+$... is

• A. $2n+2^{1-n}$
• B. $2n+2-2^{1-n}$
• C. $n+2^n$
• D. none of these

Answer 1

The correct option is B $2n+2-2^{1-n}$

Here $t_n=\frac{2^n+1}{2^{n-1}}=2+\frac{1}{2^{n-1}}$
$S=\sum _{n=1}^n(2+\frac{1}{2^{n-1}})=\sum _{n=1}^n\left(2\right)+\sum _{n=1}^n\left(\frac{1}{2^{n-1}}\right)=2n+\left[(1-\frac{1}{2^{n-1}})/(1-\frac{1}{2})\right]=2n+2-2^{1-n}$
Ans: B