Prove the following by the principle of mathematical induction: `1+3+3^2++3^(n-1)=(3^n-1)/2`

Explanation

Let `P(n):1+3+3^2+....3^(n−1)
=(3^n−1)/2​`

For `n=1`,LHS`=1`

RHS`=(3−1)/2​=1`

∴LHS=RHS

∴`P(1)` is true

Let us assume P(k) is true for some `k∈N`

i.e, `1+3+3^2+...+3^(k−1)=(3^k−1)/2`​

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