If f (x) +f (x+a) + f(x+2a) +....+ f (x+na) = constant; ∀xϵR and a>0 and f(x) is periodic,then period of f(x), is
Options:
A .  
(n+1) a
B .  
en+1a
C .  
na
D .  
ena
Answer: Option A : 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)a∴T=(n+1)a
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