$\frac{1}{7}\frac{1}{23}-\frac{1}{1009}\frac{1}{23}+\frac{1}{7}-\frac{1}{1009}+\frac{1}{7}.\frac{1}{23}.\frac{1}{1009}$ \left(\frac{1}{7}+\frac{1}{23}-\frac{1}{1009}\right)$$ \frac{1}{5}$$ +$$ \frac{1}{8}$$ +$$ \frac{1}{11}$$ +$$ \frac{1}{14}$$ +$$ +$$ \frac{1}{92}$$ +$$ \frac{1}{95}$$ A=1\frac{1}{2}\times 1\frac{1}{3}\times 1\frac{1}{4}....\times 1\frac{1}{2016}\times 1\frac{1}{2017}$$ D=3^2\times 9^2\times 243+18\times 243\times 324+723\times 729$$ \overline{53\ast }$$ \overline{\ast 471}$$ \frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{\left(3n-1\right).\left(3n+2\right)}=\frac{n}{6n+4}$$ \frac{5}{3.7}+\frac{5}{7.11}+\frac{5}{11.15}+...+\frac{5}{\left(4n-1\right).\left(4n+3\right)}=\frac{5n}{4n+3}$$ 50$$ 32$$ 24$$ 50$$ 32$$ 24$$ \in $$ \frac{x}{15}=\frac{4}{y}=\frac{-2}{5}$$ \frac{-5}{9}+\frac{-8}{15}+\frac{22}{-9}+\frac{-7}{15}<x\le \frac{-1}{3}+\frac{-1}{4}+\frac{-5}{12}$$ \frac{x-3}{4}=\frac{15}{20}$$ \begin{array}{c}C=\frac{3}{2}+{\left(\frac{3}{2}\right)}^2+{\left(\frac{3}{2}\right)}^3+....+{\left(\frac{3}{2}\right)}^{2013}\\ \iff \frac{3}{2}C=\frac{3}{2}.\left[\frac{3}{2}+{\left(\frac{3}{2}\right)}^2+{\left(\frac{3}{2}\right)}^3+....+{\left(\frac{3}{2}\right)}^{2013}\right]\\ \iff \frac{3}{2}C={\left(\frac{3}{2}\right)}^2+{\left(\frac{3}{2}\right)}^3+{\left(\frac{3}{2}\right)}^4+......+{\left(\frac{3}{2}\right)}^{2014}\\ \iff \frac{3}{2}C-C=\left[{\left(\frac{3}{2}\right)}^2+{\left(\frac{3}{2}\right)}^3+{\left(\frac{3}{2}\right)}^4+......+{\left(\frac{3}{2}\right)}^{2014}\right]-\left[\frac{3}{2}+{\left(\frac{3}{2}\right)}^2+{\left(\frac{3}{2}\right)}^3+....+{\left(\frac{3}{2}\right)}^{2013}\right]\\ \iff \frac{1}{2}C={\left(\frac{3}{2}\right)}^{2014}-\left(\frac{3}{2}\right)\\ \iff C={\left(\frac{3}{2}\right)}^{2014}.2-3\\ A=\frac{1}{2}+C={\left(\frac{3}{2}\right)}^{2014}.2-\frac{5}{2}\\ B-A=\left({\left(\frac{3}{2}\right)}^{2013}.2\right)-\left({\left(\frac{3}{2}\right)}^{2014}.2-\frac{5}{2}\right)\\ =2.{\left(\frac{3}{2}\right)}^{2013}.\left(1-\frac{3}{2}\right)+\frac{5}{2}\\ =-{\left(\frac{3}{2}\right)}^{2013}+\frac{5}{2}\end{array}$$