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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

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


 

Grade:Upto college level

2 Answers

Aman Bansal
592 Points
10 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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Thanks

Aman Bansal

Askiitian Expert

aakanksha uday
30 Points
10 years ago

hi aman

take f(x) as a periodic fnc. like sinx and a as constan quantity

it will give u ur ans...

wish u luck

 

 

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