Mathematical induction is a method of mathematical proof to used to establish that a given statement is true of all natural numbers. It consist of two step , I- Basis step and II- Induction Step. In First step we check the statement is true for n= 1 and when it is true them we proceed to step no-2 , induction step where we have to prove that given statement is true for n+1.
The simplest and most common form of mathematical induction proves that a statement involving a natural number n holds for all values of n. The proof consists of two steps:
The basis (base case): showing that the statement holds when n = 0 or n = 1.
The inductive step: showing that if the statement holds for some n, then the statement also holds when n + 1 is substituted for n.
The assumption in the inductive step that the statement holds for some n is called the induction hypothesis (or inductive hypothesis). To perform the inductive step, one assumes the induction hypothesis and then uses this assumption to prove the statement for n + 1.
Suppose the sum of first n natural number is given by : 1+2+3+….+n = n(n+1)/2
In this statement we have to prove first this statement is true for n=1 and then n= n+1 in induction step.
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