The sum of the infinite series $$513+55132+555133+$$…..

⇒We have $$S=513+55132$$........⇒$$S13=5132+55133$$........S−$$S13=513+50132+500133$$......⇒$$12S13=513+50132+$$.....⇒$$S=6536=1.81$$

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$The sum of the infinite series \frac{5}{13} + \frac{55}{13^{2}} + \frac{555}{13^{3}} + \dots . .$

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$\Rightarrow \begin{array}{l} W e h a v e S = \frac{5}{13} + \frac{55}{13^{2}} ........ \\ \Rightarrow \frac{S}{13} = \frac{5}{13^{2}} + \frac{55}{13^{3}} ........ \\ (S - \frac{S}{13}) = \frac{5}{13} + \frac{50}{13^{2}} + \frac{500}{13^{3}} ...... \\ \Rightarrow \frac{12 S}{13} = \frac{5}{13} + \frac{50}{13^{2}} + ..... \\ \Rightarrow S = \frac{65}{36} = 1.81 \end{array}$

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Geometric progression

Remember concepts with our Masterclasses.

The sum of the infinite series 513+55132+555133+…..

⇒We have S=513+55132........⇒S13=5132+55133........S−S13=513+50132+500133......⇒12S13=513+50132+.....⇒S=6536=1.81

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$The sum of the infinite series \frac{5}{13} + \frac{55}{13^{2}} + \frac{555}{13^{3}} + \dots . .$