Period of the function f ( x ) = [ x ] + [ 2 x ] + [ 3 x ] + [ 4 x ] + … + [ nx ] − 2 n ( n + 1 ) x , where n ∈ N and [ ] denotes the greatest integer function, is

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Period of the function f ( x ) = [ x ] + [ 2 x ] + [ 3 x ] + [ 4 x ] + … + [ nx ] − 2 n ( n + 1 ) x ​ , where n ∈ N and [ ] denotes the greatest integer function, is

TestHub · Accepted Answer

f ( x ) ​ = [ x ] + [ 2 x ] + … .. + [ nx ] − ( x + 2 x + … .. + nx ) = ([ x ] − x ) + ([ 2 x ] − 2 x ) + … .. + ([ nx ] − nx ) = − ({ x } + { 2 x } + … .. + { nx }) ​

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