Evaluate  $\frac+\frac+\frac+\frac+\ldots$ upto n terms

A. $2^n -n +1$

B. $n-2^ +1$

C. $n+2^ -1$

D. $2^n -n-1$

C.$n-1+2^$

Given $\frac+\frac+\frac+\frac+\ldots$
$$
\begin
& =\left(1-\frac\right)+\left(1-\frac\right)+\left(1-\frac\right)+\left(1-\frac\right)+\ldots \\
& =\mathrm-\left(\frac+\frac+\frac+\frac+\ldots \ldots \ldots+\frac\right)
\end
$$
$=\mathrm-\frac{\frac\left(1-2^{-\mathrm}\right)}{1-\frac} \quad\left[\right.$ Sum of $\mathrm=\frac{\mathrm{a}\left(1-\mathrm^{\mathrm}\right)}$ when $\left.\mathrm<1\right]$
$$
=n-1+2^
$$