Question Number 95765 by I want to learn more last updated on 27/May/20
$$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{40}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{20}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{10}}\:\:+\:\:...\:\:+\:\:\boldsymbol{\mathrm{n}}\right) \\ $$
Commented by prakash jain last updated on 27/May/20
$$\left.\frac{\mathrm{1}}{\mathrm{40}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{20}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{10}}\:\:+\frac{\mathrm{1}}{\mathrm{5}}+\frac{\mathrm{2}}{\mathrm{5}}+\frac{\mathrm{4}}{\mathrm{5}}+..\right) \\ $$$$\mathrm{You}\:\mathrm{will}\:\mathrm{never}\:\mathrm{reach}\:\mathrm{an}\:\mathrm{integer}. \\ $$$$ \\ $$$$\mathrm{There}\:\mathrm{are}\:\mathrm{infinite}\:\mathrm{way}\:\mathrm{to}\:\mathrm{interpret} \\ $$$$\mathrm{the}\:\mathrm{given}\:\mathrm{sequence}.\:\mathrm{So}\:\mathrm{you}\:\mathrm{need} \\ $$$$\mathrm{to}\:\mathrm{specify}\:\mathrm{formula}\:\mathrm{for}\:\mathrm{term}. \\ $$
Commented by I want to learn more last updated on 27/May/20
$$\mathrm{Show}\:\mathrm{any}\:\mathrm{way}\:\mathrm{sir} \\ $$
Commented by prakash jain last updated on 27/May/20
$$\mathrm{one}\:\mathrm{way} \\ $$$$\mathrm{put}\:\mathrm{all}\:\mathrm{midlle}\:\mathrm{terms}\:\mathrm{0} \\ $$$$\mathrm{sum}=\left({n}+\frac{\mathrm{1}}{\mathrm{40}}+\frac{\mathrm{1}}{\mathrm{20}}+\frac{\mathrm{1}}{\mathrm{10}}\right)×\mathrm{2} \\ $$