Question

prove that the sum of any two successive odd numbers is a multiply of 4

Answer 1

1+3=4
7+9=16
111+113=224
they all are multiplying by 4

Answer 2

Let first odd no.= 2n+1
so second is = 2n+3
therefore we get sum of these two no. is
sum =2n+1 +2n+3=mulitple of 4
=4n+4
Using PMI

Step- 1
let n=1
4n+4=4+4=8 is a multiple of 4.

Step- 2
let n=k
4n+4=4k+4

Step- 3
let n=k+1
4n+4=4(k+1)+4
=4k+4+4
=4k+8
=4(k+2) is a multiple of 4..

Hence result is true for all value of n