Question

The sum of the co-efficient in the expansion of `(1-2x+5x^2)^n` is 'a' and sum of the co-efficients in the expansion of `(1+x)^(2n)` is b. What is the relation between a and b?

Answer 1

The sum of the coefficients in an expansion can be obtained by putting the value of each variable equals to 1.

So the sum of the co-efficient in the expansion of `(1-2x+5x^2)^n` will be

`(1-2*1+5*1^2)^n=a`

`=>4^n=a`

Similarly the sum of the co-efficients in the expansion of `(1+x)^(2n)` will be

`(1+1)^(2n)=b`

`=>2^(2n)=b`

`=>(2^2)^n=b`

`=>4^n=b`

So the relation between a and b is `a=b`