`(1-x)^(-4)` में विस्तार में (r+1)वाँ पद है

Options

A. `(x^(r))/(r!)`
B. `((r+1)(r+2)(r+3))/(6) x^(r)`
C. `((r+2)(r+3))/(2)x^(r)`
D. इनमें से कोई नहीं

Answer

B

Explanation

`T_(r+1)`
`=([(-4)(-4-1)(-4-2)...(-4-r+3)(-4-r+2).(-4-r+1)])/(r!)(-x)^(r)`
`=(4.5.6.7...r(r+1)(r+2)(r+3))/(r!).x^(r)`
`=(4.5.6.7...r(r+1)(r+2)(r+3))/(1.2.3...(r-1)r).x^(r)`
`=((r+1)(r+2)(r+3))/(1.2.3).x^(r)`
`=((r+1)(r+2)(r+3))/(6).x^(r)`