Mathematics - Sequence & Series Question with Solution | TestHub

Let $t_r=\frac{5^{100}}{25^r+5^{100}}$. Then $t_r+t_{100-r}=1$ (check: $t_1+t_{99}=\frac{5^{100}}{25+5^{100}}+\frac{5^2}{5^{100}+5^2}=1$ ). Pairing $t_1+t_{99},\dots ,t_{49}+t_{51}$ gives 49, and $t_{50}=\frac{5^{100}}{25^{50}+5^{100}}=\frac{1}{2}$. $S=49+\frac{1}{2}=49.5$, so $[S]=49$. ZZZ DUMMY - DO NOT IMPORT \end{document}