Question

If a and b are the respective coefficients of x^m and x^n in the expansion of (1+X)^m+n then,

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Answer 1

Answer:

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Answer 2

Answer:

Given -

a and b are the coefficients of x^m and x^n in the expansion of (1+x)^m+n

Solution -

Using Binomial theorem,

$({1 + x})^{m + n} = ( \frac{m + n}{k} )x^{k}$

${t}^{k - 1} = ( \frac{m + n}{k} )x ^{k}$

Coefficient of x^m, a= (m - n) =

$\frac{(m + n)}{m(m + n - m)}$

$a = \frac{(m + n)}{mn}$

Coefficient of x^n, b= (m + n) =

$\frac{(m + n)}{n(m + n + m)}$

$b = \frac{(m + n)}{mn} + \frac{(m + n)}{mn}$

$= > a + b = 2a$

$= > b = 2a - a$

$= > b = a$

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