Prove the following by using the principle of mathematical induction for all `n in N`:`1/2+1/4+1/8+...+1/(2^n)=1-1/(2^n)`

Explanation

Given,

P(n),`1​+1/4​+1/8​+....+1​/(2^n)=1−1/2^n​`


For n=1

`P(1)=1/2`​, which is true.


Let P(k) be true for k

`1/2​+1/4​+1/8​+....+1/2^k​=1−1/2^k`​....(i)

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