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Question

If f (x) +f (x+a) + f(x+2a) +....+ f (x+na) = constant; x ϵR and a>0 and f(x) is periodic,then period of f(x), is

A
(n+1) a
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B
en+1a
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C
na
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D
ena
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Solution

The correct option is A (n+1) a
f(x)+f(x+a)+f(x+2a)+....+f(x+na)=k
replacing x=x+a
f(x+a)+f(x+2a)+....+f(x+(n+1)a)=k
On subtracting second equation from first one -
f(x)f(x+(n+1)a)=0f(x)=f(x+(n+1)aT=(n+1)a

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