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prove that 1+5+9+ . . .+(4n-3)=n(2n-1), ...

prove that 1+5+9+ . . .+(4n-3)=n(2n-1), for all natural number n.

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To prove that \( 1 + 5 + 9 + \ldots + (4n - 3) = n(2n - 1) \) 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 \( n = 1 \). \[ LHS = 1 = 1(2 \cdot 1 - 1) = 1(1) = 1 \] ...
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