If a and b denote respectively the coefficients of xm and xn in the expansion of 1-xm-n- then write the relation between a and b-

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Standard XII

Mathematics

Multinomial Expansion

If a and b de...

Question

If a and b denote respectively the coefficients of x^m and xⁿ in the expansion of ${(1 + x)}^{m + n}$ , then write the relation between a and b.

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Solution

$Coefficient of x^{m} in the given expansion = {}^{m + n}C_{m} = a Coefficient of x^{n} in the given expansion = {}^{m + n}C_{n} = b ∴ a = b [∵ {}^{m + n}C_{m} = {}^{m + n}C_{n}]$

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If a and b denote respectively the coefficients of xm and xn in the expansion of 1+xm+n, then write the relation between a and b.

Coefficient of xm in the given expansion = Cmm+n =aCoefficient of xn in the given expansion = Cnm+n =b∴a=b ∵Cmm+n =Cnm+n

If a and b denote respectively the coefficients of x^m and xⁿ in the expansion of ${(1 + x)}^{m + n}$ , then write the relation between a and b.

$Coefficient of x^{m} in the given expansion = {}^{m + n}C_{m} = a Coefficient of x^{n} in the given expansion = {}^{m + n}C_{n} = b ∴ a = b [∵ {}^{m + n}C_{m} = {}^{m + n}C_{n}]$