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Let [x] denotes greatest integer Then equal to Possible Answers Selected Possible Answer x/2 x/3 0 x/4




Let [x] denotes greatest integer Then
equal to




Possible Answers























Selected Possible Answer



x/2







x/3







0







x/4





Grade:12

2 Answers

satish prakash garg
16 Points
11 years ago

x/3 is ans

[x]=x-{x}

and 

sum of sq. of n no. are  n*(n+1)*(2n+1)/6

Askiitians Expert Soumyajit IIT-Kharagpur
28 Points
11 years ago

Dear Geetika Chouhan,

Ans:-Now the given function is a box function. So [x]=x-{x}

where {x}=fractional part of x whose value lie between 0 and 1

So writing all the box functions like this we get

the series (1²x+2²x+...........n²x) -K where K is a constant whose max value is n

Hence the sum is =  xn(n+1)(2n+1)/6   -n

dividing it by n^3 we get

Sum=x(1+1/n)(2+1/n)/6        -1/n²

Taking n→∞ We get

Sum=x/3(ans)

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