Mathematics - Binomial Theorem Question with Solution | TestHub

$\left\{{}^n{C}_{0}100^n-{}^n{C}_1\cdot 100^{n-1}+\dots \dots \dots -{}^n{C}_n\right\}$ Because n is odd $=100\{{}^n{C}_0.100^{n-1}-{}^n{C}_1.100^{n-2}+\dots \dots \dots -$ ${}^n{C}_{n-2}\cdot 100+{}^n{C}_{n-1}\}$ $=100\times$ integer

whose units place is different from 0

$[{\because }^n{C}_{n-1}=n$,has odd digit at unit place $]$

∴ There are two zeros at the end of the sum $99^n+1$