prove that 1+2+22+23+...+2n=2n-1-1,is true for all natural numbers n.

dear student

1+2+22+23+.....+2n=2n-1-1the above equation is not correctasfor n=1LHS=1RHS=21-1-1=0the correct expression should be1+2+22+23+.....+2n-1=2n-1for n=1LHS=1RHS=21-1=2-1=1 assuming true for n=nfor n=n+1, we haveLHS=1+2+22+23+.....+2n-1+2n=2n-1+2n=2.2n-1=2n+1-1so true for n+1hence proved

regards

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