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Prove that1+2+2^(2)+ . . .+2^(n)=2^(n+1)...

Prove that`1+2+2^(2)+ . . .+2^(n)=2^(n+1)-1`, for all natural number n.

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To prove the statement \(1 + 2 + 2^2 + \ldots + 2^n = 2^{n+1} - 1\) for all natural numbers \(n\), we will use the principle of mathematical induction. ### Step 1: Base Case We start by checking the base case when \(n = 1\). **LHS:** \[ 1 + 2 = 3 ...
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