Question
Question: Period of f(x) = [x] + [2x] + [3x] + [4x] + .... + [nx] −<img src="https://cdn.pureessence.tech/canv...
Period of f(x) = [x] + [2x] + [3x] + [4x] + .... + [nx] −
where n ∈ N and [.] denotes the greatest integer function, is
A
n
B
1
C
1/n
D
None of these
Answer
1
Explanation
Solution
f(x) = [x] + [2x] + [3x] + .... + [nx]
− (x + 2x + 3x + ....nx)
= -({x} + {2x} + {3x}+......+ {nx})
Period of f(x) = L.C.M. 