Question

2.
16. the period of tan(x+2x+3x +...+ nx) is​

Answer 1

Answer:

$\frac{2\pi}{n(n + 1)}$

Step-by-step explanation:

Given,

tan(x+2x+3x +...+ nx)

so,

tan[X(1+2+3+...+n)]

$tan[x(1+2+3+...+n)] \\ = \frac{\pi}{ \frac{n(n + 1)}{2} } = \frac{2\pi}{n(n + 1)}$

note that

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