Exercise · ZW-MATHEMATICAL-INDUCTION-002 · ★☆☆ Basic

To prove \(2+4+\cdots+2n=n(n+1)\), in the base case \(n=1\) both sides equal:

Choose one option.

Show answer

A. \(2\)

Explanation

With \(n=1\): left side \(2\), right side \(1\cdot2=2\).

Review the concept: Mathematical induction

Mathematical induction proves that a property \(P(n)\) holds for every integer \(n\ge n_0\): one checks the base case \(P(n_0)\) and proves that, for each \(k\ge n_0\), \(P(k)\) implies \(P(k+1)\).

\[\big[P(n_0)\wedge\forall k\ge n_0\,(P(k)\Rightarrow P(k+1))\big]\Rightarrow\forall n\ge n_0\,P(n)\]

More practice problems: mathematical induction

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