It is given that$\displaystyle sn=2*2+3*2^2+4*2^2+........ +(n+1)*2^n$

a) By first considering the values of $\displaystyle \frac{S1}{1}$,$\displaystyle \frac{S2}{2}$,$\displaystyle \frac{S3}{3}$,$\displaystyle \frac{S4}{4}$ and making a conjecture for a formula for $\displaystyle \frac{Sn}{n}$, make a conjecture for a formula for Sn.

b) Use induction to prove that your conjecture is correct.

For a) i did $\displaystyle S1=4, S2=6, S3=8$

so the conjecture for $\displaystyle Sn=2n+2$

b) $\displaystyle S1=4$, $\displaystyle S1=2*1+2=4$

so n=1 is true.

$\displaystyle Sk=2k+2$

$\displaystyle Sk+1=2(k+1)+2 = 2k+4$

what do i do next? or how to i prove $\displaystyle Sk+1=2k+4$

thanks.