Prove that sum of 2+4+8+ - - - - +2^n= -2(1-2^n).

 Given that 2+4+8+- - - - +2^n

This expression is a geometrical progression (G.P) . 

Let 'a' be the first term and 'r' the common ratio. 

Here a=2 and r=4/2 =8/4 = - - - =2^n/2^(n-1)=2

Sum of n terms of a G.P; S_n=a(1-r^n)/(1-r).

=> S_n=2(1-2^n)/(1-2)

=> S_n= -2(1-2^n).

Hence the result proved.