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Find the value of

$$\dfrac{3}{4}+\dfrac{3}{28}+\dfrac{3}{70}+\dfrac{3}{130}+...............+\dfrac{3}{9700}$$

Fast.

Note by Sai Ram
1 year ago

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$$\frac{3}{4} + \frac{3}{28} + \frac{3}{70} + \frac{3}{130} + \ldots + \frac{3}{9700} \\ \frac{3}{1\times 4}+\frac{3} {4\times 7}+\frac{3}{7\times 10}+\frac{3}{10\times 13}+\ldots+\frac{3}{97\times 100} \\ \left(1-\frac{1} {4}\right)+\left(\frac{1} {4}-\frac{1}{7}\right)+\left(\frac{1}{7}-\frac{1} {10}\right)+\ldots+\left(\frac{1}{97}-\frac{1} {100}\right) \\ 1-\frac{1} {100}=\frac{99} {100}=\boxed{0.99}$$ · 1 year ago

Yay to the Telescoping Series - Sum! Staff · 1 year ago

Sir, is there another easy way ? · 1 year ago

Thank you very much.

Is there another way ? · 1 year ago