Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

f(x)=[x] + [2x] + [3x] +........+[nx] – nx(n+1)/2 where [.] denotes greatest integer function. Find the period of the function above. 0 clue on how to begin with this one, would appreciate some tips on how to approach periodic functions within series, I constantly do badly at these type of problems

f(x)=[x] + [2x] + [3x] +........+[nx] – nx(n+1)/2

where [.] denotes greatest integer function. Find the period of the function above.
 
0 clue on how to begin with this one, would appreciate some tips on how to approach periodic functions within series, I constantly do badly at these type of problems

Grade:

2 Answers

Havishma Haranath
32 Points
5 years ago
I think the answer is onr.
We generally know that [x+integer]=[x]+integer
let’s consider f(x+1)= [x+1]+[2(x+1)]+....+[n(x+1)]-n(x+1)(n+1)/2
solving which we get f(x+1)=[x]+1+[2x]+2+....+[nx]+n-n(n+1)/2-nx(n+1)/2
since 1+2+3+...+n=n(n+1)/2
we get f(x+1)=f(x)
similarly we can also show that f(x)=f(x+1)=f(x+2)=..f(x+any integer)
but since period must be the least posibble number
period is !
Havishma Haranath
32 Points
5 years ago
*period is 1

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free

10th iCAT Scholarship Test Registration Form