Question Number 107092 by 175mohamed last updated on 08/Aug/20
Commented by Dwaipayan Shikari last updated on 08/Aug/20
$$\mathrm{S}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$
Commented by hgrocks last updated on 09/Aug/20
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Answered by Dwaipayan Shikari last updated on 08/Aug/20
$$\mathrm{First}\:\mathrm{term} \\ $$$$\frac{\mathrm{1}}{\mathrm{6}}=\frac{\mathrm{3}−\mathrm{2}}{\mathrm{3}.\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\mathrm{second}\:\mathrm{term} \\ $$$$\frac{\mathrm{7}−\mathrm{3}}{\mathrm{7}.\mathrm{3}}=\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{7}} \\ $$$$..\frac{\mathrm{25}−\mathrm{7}}{\mathrm{25}.\mathrm{7}}=\frac{\mathrm{1}}{\mathrm{7}}−\frac{\mathrm{1}}{\mathrm{25}} \\ $$$$\frac{\mathrm{121}−\mathrm{25}}{\mathrm{25}.\mathrm{121}}=\frac{\mathrm{1}}{\mathrm{25}}−\frac{\mathrm{1}}{\mathrm{121}} \\ $$$$\mathrm{S}=\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{7}}+\frac{\mathrm{1}}{\mathrm{7}}−\frac{\mathrm{1}}{\mathrm{25}}+\frac{\mathrm{1}}{\mathrm{25}}−\frac{\mathrm{1}}{\mathrm{121}}+… \\ $$$$\mathrm{S}=\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\mathrm{term}\:\mathrm{n}\rightarrow\mathrm{0}\left(\:\mathrm{n}\rightarrow\infty\right) \\ $$
Commented by Dwaipayan Shikari last updated on 08/Aug/20
$$\mathrm{It}\:\mathrm{is}\:\mathrm{just}\:\mathrm{an}\:\mathrm{assumption}.\:\mathrm{Is}\:\mathrm{it}\:\mathrm{right}? \\ $$