Question-189901

Question Number 189901 by cherokeesay last updated on 23/Mar/23

Answered by BaliramKumar last updated on 24/Mar/23

4. (i) 2[(1/2) − (1/∞)] = 2[(1/2) − 0] = 1

$$\mathrm{4}.\:\left(\mathrm{i}\right)\:\mathrm{2}\left[\frac{\mathrm{1}}{\mathrm{2}}\:−\:\frac{\mathrm{1}}{\infty}\right]\:=\:\mathrm{2}\left[\frac{\mathrm{1}}{\mathrm{2}}\:−\:\mathrm{0}\right]\:=\:\mathrm{1} \\ $$

Answered by talminator2856792 last updated on 24/Mar/23

3) (1/5) + (2/6) + (2^2 /7) + (2^3 /8) + (2^4 /9) + ..... > (1/5) + (2/(5∙2)) + (2^2 /(5∙2^2 )) + (2^3 /(5∙2^3 )) + (2^4 /(5∙2^4 )) + ..... = (1/5) + (1/5) + (1/5) + (1/5) + (1/5) + ..... = ∞ diverges.

$$\left.\:\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{2}}{\mathrm{6}}\:+\:\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{7}}\:+\:\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{8}}\:+\:\frac{\mathrm{2}^{\mathrm{4}} }{\mathrm{9}}\:+\:…..\:\:>\:\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{2}}{\mathrm{5}\centerdot\mathrm{2}}\:+\:\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{5}\centerdot\mathrm{2}^{\mathrm{2}} }\:+\:\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{5}\centerdot\mathrm{2}^{\mathrm{3}} }\:+\:\frac{\mathrm{2}^{\mathrm{4}} }{\mathrm{5}\centerdot\mathrm{2}^{\mathrm{4}} }\:+\:…..\:\:\: \\ $$$$\:\:\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:….. \\ $$$$\:\:\:\:\:\:=\:\infty \\ $$$$\:\:\:\:\:\:\mathrm{diverges}. \\ $$

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Question-189901

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