How To Write A Mathematical Induction Proof Complete Guide

This step is called the induction step. It has only 2 steps. Thus 1 holds for n k 1 and the proof of the induction step is complete.

Show that the statement holds for the smallest natural number n 0.

0 0 0 1 2. Displaystyle 012cdots n tfrac n n1 2 We give a proof by induction on n. I k 1 kk 1 2 k 1 by induction hypothesis kk 1 2k 1 2 by algebra k 1k 1 1 2 by algebra. 0 1 2 n n n 1 2.