7. binomial theoram — ગણિત ધોરણ 11 સાયન્સ — Question

= $1 + 10 + {10^2} + ..... + {10^{90}}$

= $\frac{{{{10}^{91}} - 1}}{{10 - 1}} = \frac{{{{({{10}^7})}^{13}} - 1}}{{10 - 1}}$= $\frac{{{t^{13}} - 1}}{9}$, where $t = {10^7}$

= $\left( {\frac{{t - 1}}{9}} \right)\,({t^{12}} + {t^{11}} + ..... + t + 1)$

= $\left( {\frac{{{{10}^7} - 1}}{{10 - 1}}} \right)\,(1 + t + {t^2} + .... + {t^{12}})$

$ = (1 + 10 + {10^2} + .... + {10^6})(1 + t + {t^2} + ... + {t^{12}})$

 $111.....1(91\,\,{\rm{times)}}$ is a composite number.