First slide

Binomial theorem for positive integral Index

Question

In the binomial expansion of $(1 + a)^{m + n}$ $n,$ if the coefficients of $a^{m}$ and $a^{n}$ are $A$ and $B$ respectively, then

Moderate

A

$A = B$
B

$m A = n B$
C

$n A = m B$
D

$A = 2 B$

Solution

In the binomial expansion of $(1 + a)^{n + n}$ ,we have
A = Coefficient of $a^{m} =^{m + n} C_{m} = \frac{(m + n)!}{m! n!}$
and ,
B = Coefficient of $a^{n} =^{m + n} C_{n} = \frac{(m + n)!}{m! n!}$
Clearly, A = B.

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