wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
na
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
e^{na}
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
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

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Periodic Functions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon