A small block slides down on a smooth inclined plane, starting from rest at time t=0 .Let S_n be the distance travelled by the block in the interval t=n-1 to t=n. Then, the ratio $\frac{S_{n}}{S_{n + 1}}$ is :

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$\frac{2 n + 1}{2 n - 1}$

$\frac{2 n}{2 n - 1}$

$\frac{2 n - 1}{2 n}$

$\frac{2 n - 1}{2 n + 1}$

answer is C.

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Detailed Solution

$\begin{array}{l} S_{n} = 0 + \frac{1}{2} a (2 n - 1) \\ S_{n + 1} = 0 + \frac{1}{2} a (2 (n + 1) - 1) \\ = \frac{1}{2} a (2 n + 1) \\ \frac{S_{n}}{S_{n + 1}} = \frac{(2 n - 1)}{(2 n + 1)} \end{array}$

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