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Geetika Chouhan Grade: 12

Let [x] denotes greatest integer Then
equal to

Possible Answers

Selected Possible Answer

x/2

x/3

0

x/4

7 years ago

## Answers : (2)

satish prakash garg
16 Points

x/3 is ans

[x]=x-{x}

and

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

7 years ago
Askiitians Expert Soumyajit IIT-Kharagpur
28 Points

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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Askiitians Experts

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7 years ago
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