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if A be the sum of odd terms and B the sum of even terms in the expansion of (x+a) to the power n then rove that 1. A square-B square = (x square-a square)to the power n

if A be the sum of odd terms and B the sum of even terms in the expansion of (x+a) to the power n then rove that
1. A square-B square = (x square-a square)to the power n

Grade:

2 Answers

Varna Sambhangi
33 Points
8 years ago

A=nc1 x^n-1+nc3x^n-3.......

B=nc0x^n+nc2x^n-2........

Now,A+B=(x+a) and B-A=(x-a)

Therefore it sud be (A^2-B^2)=(x^2-a^2)

Chetan Mandayam Nayakar
312 Points
8 years ago

use the principle of mathematical induction

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