If $$f(x)=$$$$sin$$⁡$$x+$$$$tan$$⁡$$x2+$$$$sin$$⁡$$x22+$$$$tan$$⁡$$x23+$$…$$+$$$$sin$$⁡$$x2n$$−$$1+$$$$tan$$⁡$$x2n$$ is a periodic function with period kπ, then $$k=$$

Question

If $$f(x)=$$$$sin$$⁡$$x+$$$$tan$$⁡$$x2+$$$$sin$$⁡$$x22+$$$$tan$$⁡$$x23+$$…$$+$$$$sin$$⁡$$x2n$$−$$1+$$$$tan$$⁡$$x2n$$ is a periodic function with period kπ, then $$k=$$

Infinity Learn · Accepted Answer

sinx,$$sinx22$$,…,$$sinx2n$$−$$1$$ are periodic functions with         period $$2$$π,$$23$$π,$$25$$π,…,$$2n$$π, respectively and $$tanx2$$,$$tanx23$$ ,$$tanx25$$,…,$$tanx2n$$ are periodic functions with period $$2$$π ,$$23$$π,$$25$$π,…,$$2n$$π, respectively. L.C.M. of $$2$$π,$$23$$π,$$25$$π,…$$2n$$π is $$2n$$π .Hence $$f(x)$$ is a periodic function with period $$2n$$π . ∴$$k=2n$$

$If f (x) = \sin x + \tan \frac{x}{2} + \sin \frac{x}{2^{2}} + \tan \frac{x}{2^{3}} + \dots + \sin \frac{x}{2^{n - 1}} + \tan \frac{x}{2^{n}} is a periodic function with period k π, then k =$

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If f(x)=sin⁡x+tan⁡x2+sin⁡x22+tan⁡x23+…+sin⁡x2n−1+tan⁡x2n is a periodic function with period kπ, then k=

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$If f (x) = \sin x + \tan \frac{x}{2} + \sin \frac{x}{2^{2}} + \tan \frac{x}{2^{3}} + \dots + \sin \frac{x}{2^{n - 1}} + \tan \frac{x}{2^{n}} is a periodic function with period k π, then k =$