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Questions  

 If k=0nf(x+ka)=0, where a>0, then the period of f(x) is

a
a
b
(n+1)a
c
an+1
d
f(x) is non-periodic

detailed solution

Correct option is B

Given f(x)+f(x+a)+….+f(x+an)=0 … (1) Replacing x by x+a , we get  f(x+a)+f(x+2a)+…+f{x+a(n+1)}=0−−−2 Subtracting ( 2 ) from (1), we get f(x)−f(x+a(n+1)}=0Thus, f(x) is periodic with period a(n+1) .

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