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The period of f(x)=[x]+[2x]+[3x]+[4x]+[n...

The period of `f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x ,` where `n in N ,` is (where `[dot]` represents greatest integer function). (a) `n` (b) 1 (c) `1/n` (d) none of these

A

n

B

1

C

`(1)/(n)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=[x]+[2x]+[3x]+ …+[nx] -(x+2x+3x+ … + nx)`
`= -({x}+{2x}+{3x}+ … +{nx})`
Period of `f(x)=LCM (1,(1)/(2),(1)/(3), …, (1)/(n))=1.`
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