Mathematics - Binomial Theorem Question with Solution | TestHub

In${\left(1+x\right)}^n$, if$n$is even, then the middle term is${\left(\frac{n}{2}+1\right)}^{th}$term.

So, Coefficient of middle term in $(1+x{)}^{20}={}^{20}C_{10}$

In${\left(1+x\right)}^n$, if$n$is odd, then the middle term is${\left(\frac{n+1}{2}\right)}^{th} \& {\left(\frac{n+3}{2}\right)}^{th}$term.

So, Sum of Coefficient of two middle terms in

$(1+x{)}^{19}={}^{19}C_9+{}^{19}C_{10}$

So required ratio $=\frac{{}^{20}C_{10}}{{}^{19}C_9+{}^{19}C_{10}}=\frac{{}^{20}C_{10}}{{}^{20}C_{10}}=1$