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In the expansion of (a+b)^(n), if two co...

In the expansion of `(a+b)^(n)`, if two consecutive terms are equal, then which of the following is/are always integer ?

A

`((n+1)b)/(a+b)`

B

`((n+1)a)/(a+b)`

C

`(na)/(a-b)`

D

`(na)/(a+b)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
We have `(a+b)^(n)`
`(T_(r+1))/(T_(r)) = (n-r+1)/(r ) . b/a = 1`
`:. (n+1)b-r = ar`
`:. r = -((n+1)b)/(a+b)` is integer
Also, considering `(b+a)^(n)`.
`(T_(r+1))/(T_(r)) = (n-r+1)/(r ) . a/b = 1`
`:. R = ((n+1)a)/(a+b)` is integer
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