The ratio of the coefficient of the middle term in the expansion of $(1+x)^{20}$ and the sum of the

Question

The ratio of the coefficient of the middle term in the expansion of $(1+x)^{20}$ and the sum of the coefficients of two middle terms in expansion of $(1+x)^{19}$ is

Professor PC Thomas Classes · Answer

(1) : Coefficient of middle term in the expansion of $(1+x)^{20}$ is ${ }^{20} C_{10}$.\ Coefficients of two middle terms in the expansion of $(1+x){ }^{19}$ are ${ }^{19} C_{9}$ and ${ }^{19} C_{10}$.\ $	herefore \quad$ Required ratio $$ =\frac{{ }^{20} C_{10}}{{ }^{19} C_{9}+{ }^{19} C_{10}}=\frac{{ }^{20} C_{10}}{{ }^{20} C_{10}}=1 $$