Question

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

• A. (n+1) a
• B.
• C. na
• D. e^{na}

Answer 1

The correct option is A (n+1) a

$f\left(x\right)+f(x+a)+f(x+2a)+....+f(x+na)=kreplacingx=x+af(x+a)f(x+2a)+....+f(x+(n+1\left)a\right)=kf\left(x\right)-f(x+(n+1\left)a\right)=0f\left(x\right)=f(x+(n+1)a\therefore T=(n+1)a$