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By using principle of mathematical induc...

By using principle of mathematical induction, prove that 2+4+6+….2n=n(n+1), `n in N`

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To prove that \( 2 + 4 + 6 + \ldots + 2n = n(n + 1) \) for all \( n \in \mathbb{N} \) using the principle of mathematical induction, we will follow these steps: ### Step 1: Base Case We need to verify the statement for the base case \( n = 1 \). **Calculation:** \[ \text{LHS} = 2 \quad (\text{since } 2 \cdot 1 = 2) ...
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