Question

Find the coefficient of x^12 in (1-x^2)^-5 what can you set about the coefficient of x^17

Answer 1

Answer with explanation:

The expansion of

`(1+x)^n=1 + nx +(n(n-1))/(2!)x^2+(n(n-1)(n-2))/(3!)x^3+......`

where,n is a positive or negative , rational number.

Where, -1< x < 1

Expansion of

`(1-x^2)^(-5)=1-5 x^2+((5)* (6))/(2!)x^4-(5* 6* 7)/(3!)x^6+(5* 6* 7* 8)/(4!)x^8-(5* 6* 7* 8* 9)/(5!)x^(10)+(5* 6* 7* 8* 9* 10)/(6!)x^(12)+....`

Coefficient of
`x^(12)` in the expansion of
`(1-x^2)^(-5)` is

`=(5* 6* 7* 8* 9* 10)/(6!)\\\\=(15120)/(6* 5 * 4* 3 * 2 * 1)\\\\=(151200)/(720)\\\\=210`

⇒As the expansion
`(1-x^2)^(-5)` contains even power of x , so there will be no term containing
`x^(17)`.