Grade Upto college levelDifferential Calculus

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

ANAM V. RANGA REDDY

14 Years agoGrade Upto college level

2 Answers

Aman Bansal

Approved Tutor Answer14 Years ago

Dear Ranga,

Its given that

f(x)+f (x+a) + f (x+2a) + …. +f(x+na) = k(constant)

Also ,

f (x+a) + f (x+2a) + …. +f(x+na)+f(x=(n+1)a) = k(constant)

subtracting eq. 2 from 1:

=> F(x)= f(x+(n+1)a)

Thus period is (n+1)a

Best Of luck

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