Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

The principle of mathematical induction

Suppose there is a given statement  P(n)involving the natural number n such that

(i) The statement is true for n=1, i.e., P(1) is true and,

(ii) If the statement is true for  n=k, (K \epsilon N), then the statement is also true for n=K+1 i.e., P(K) true  \implies  P (K+1) true then P(n) is true for all n\in N.

If  P(n) is a statement such that

(ii)  P(m) ,  P(m+1) ,…,  P(m+K-1) are true  \implies P(m+K) is true then  P(n) is true  \forall n \in N.

(i)  P(1), P(2) ,…,  P(k) are true

If  P(n) be a statement such that

(i)  P(r) is true

(ii) P(r) ,  P(r +1),..., P(m) are true \implies P(m+1) is true

then P(n) is true  \forall \ n \geq r, n \in \ N

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