Question Number 188416 by 073 last updated on 01/Mar/23
Answered by manxsol last updated on 01/Mar/23
![Σ=(1/3^2 )+(1/3^3 )+....... Σ=(1/3)[(1/3)+(1/3^2 ).......] 3Σ=(1/3)+Σ 2Σ=(1/3) Σ=(1/6)](Q188422.png)
$$\Sigma=\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }+....... \\ $$$$\Sigma=\frac{\mathrm{1}}{\mathrm{3}}\left[\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }.......\right] \\ $$$$\mathrm{3}\Sigma=\frac{\mathrm{1}}{\mathrm{3}}+\Sigma \\ $$$$\mathrm{2}\Sigma=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\Sigma=\frac{\mathrm{1}}{\mathrm{6}} \\ $$