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.
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