Find the period of the function f(x) = $$e^{x-[x]+|cos\pi x|+|cos2\pi x|+ ….. + |cosn\pi x|}$$

Solution :

f(x) = $$e^{x-[x]+|cos\pi x|+|cos2\pi x|+ ….. + |cosn\pi x|}$$

Period of x – [x] = 1

Period of $$|cos\pi x|$$ = 1

Period of $$|cos2\pi x|$$ = $$1\over 2$$

……………………………….

Period of $$|cosn\pi x|$$ = $$1\over n$$

So period of f(x) will be L.C.M of all period = 1.

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