Question Number 189901 by cherokeesay last updated on 23/Mar/23
Answered by BaliramKumar last updated on 24/Mar/23
$$\mathrm{4}.\:\left(\mathrm{i}\right)\:\mathrm{2}\left[\frac{\mathrm{1}}{\mathrm{2}}\:−\:\frac{\mathrm{1}}{\infty}\right]\:=\:\mathrm{2}\left[\frac{\mathrm{1}}{\mathrm{2}}\:−\:\mathrm{0}\right]\:=\:\mathrm{1} \\ $$
Answered by talminator2856792 last updated on 24/Mar/23
$$\left.\:\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{2}}{\mathrm{6}}\:+\:\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{7}}\:+\:\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{8}}\:+\:\frac{\mathrm{2}^{\mathrm{4}} }{\mathrm{9}}\:+\:…..\:\:>\:\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{2}}{\mathrm{5}\centerdot\mathrm{2}}\:+\:\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{5}\centerdot\mathrm{2}^{\mathrm{2}} }\:+\:\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{5}\centerdot\mathrm{2}^{\mathrm{3}} }\:+\:\frac{\mathrm{2}^{\mathrm{4}} }{\mathrm{5}\centerdot\mathrm{2}^{\mathrm{4}} }\:+\:…..\:\:\: \\ $$$$\:\:\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:….. \\ $$$$\:\:\:\:\:\:=\:\infty \\ $$$$\:\:\:\:\:\:\mathrm{diverges}. \\ $$