Periodic summation

If f(x)+f(x+a)+f(x+2a)...f(x+na)=0,where a>o,, then the period of f(x) is what?
a> a
b> (n+1)a
c> a/(n+1)
d> Non-periodic
Please show me the method, sir.

ps.:by the way, nishanta sir, i found your techniques to find period quite useful.thanks to your technique i could find easily the period of f(x)=2 raised to the power (sin3(3.14x)+{x}), where {} is a fractional part function. Thank you

3 Answers

1
Ronald Clement ·

i think answer is B.

1357
Manish Shankar ·

put x=x-a and subtract from first

you will get f(x-a)=f(x+na)

now put x=x+a

this might solve your problem

1
Nikhil Bajoria ·

oh yes sir..thanks for the method..thank you ronald also for your tym and effort..

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