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Q.

The period of $\sin (x + 2 x + 3 x + ....... + n x)$ is

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a

$π$

b

$\frac{2 π}{n (n + 1)}$

c

$\frac{4 π}{n (n + 1)}$

d

$\frac{4 π}{n (n - 1)}$

answer is D.

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Detailed Solution

$f (x) = \sin (x + 2 x + 3 x + ....... + n x)$

$= \sin x (\frac{n (n + 1)}{2})$

Period $= \frac{2 π}{\frac{n (n + 1)}{2}} = \frac{4 π}{n (n + 1)}$

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