Question

By mathematical inductionbprove that 1+3+5+------+(2n-1)=n2

Answer 1

Answer:

7 is the answer and it is odd

Answer 2

Step-by-step explanation:

1+3+5+7+.......+(2n-1)=n²

Case 1:-Assume n=1

L.H.S=1 R.H.S=1²=1

L.H.S.=R.H.S=1

It's true for n=1

Let n=k

Equation becomes

1+3+5+7+.....+(2k-1)=k²

Case 2:-n=k+1

L.H.S=1+3+5+7+.......+2k-1+(2k+1)

=k²+2k+1

=(k+1)²

R. H. S=(n)²=(k+1)²

L. H. S=R. H. S

Hence proved by mathametical induction.