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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

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2 Answers

Havishma Haranath
32 Points
7 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
7 years ago
*period is 1

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