Find out if $\sum _{k=1}^{\mathrm{\infty}}\frac{k+1}{{2}^{k}}$ converges

I have split it into

$$\sum _{k=1}^{\mathrm{\infty}}\frac{k+1}{{2}^{k}}=\sum _{k=1}^{\mathrm{\infty}}\frac{k}{{2}^{k}}+\sum _{k=1}^{\mathrm{\infty}}\frac{1}{{2}^{k}},$$

and applied the geometric series to the second part of the sum. But how do I deal with the first one to find the limit?

I have split it into

$$\sum _{k=1}^{\mathrm{\infty}}\frac{k+1}{{2}^{k}}=\sum _{k=1}^{\mathrm{\infty}}\frac{k}{{2}^{k}}+\sum _{k=1}^{\mathrm{\infty}}\frac{1}{{2}^{k}},$$

and applied the geometric series to the second part of the sum. But how do I deal with the first one to find the limit?