No.21

Mathematical induction is a form of mathematical proof. There are two steps of mathematical induction:
1. Prove the statement is true at the starting point.
2. Assume the statement is true for n. Prove the statement is true for n+1.
Example: 1+3+5+7+...+(2n-1)=n^2
Step1 n=1
    LHS=1
    RHS=1^2=1
Since LHS=RHS is true for n=1
Step2 assume true for n. Show true for n+1
1+3+5+...+(2n+1)=(n+1)^2
    LHS=1+3+5+...+(2n-1)+(2n+1)
           = n^2+ 2n+1
    RHS=(n+1)^2
Since LHS=RHS is true for n+1
Hence the statement is true for all n element of natural number.