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

Question

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

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)`

Monjur Alahi

6 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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

6 views Answered 2023-02-05 15:29