If a and B Denote Respectively the Coefficients of Xm and Xn in the Expansion of ( 1 + X ) M + N , Then Write the Relation Between a and B. - Mathematics

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

Solution

$\text{ Coefficient of } x^m \text{ in the given expansion } = ^t{m + n}{}{C}_m = a$

$\text{ Coefficient of } x^n \text{ in the given expansion } = ^{m + n}{}{C}_n = b$

$\therefore a = b \left[ \because^{m + n}{}{C}_m = ^{m + n}{}{C}_n \right]$

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Q 6 | Page 45