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lim(n to oo)((1)/(n^2)+(2)/(n^2)+(3)/(n^...

`lim_(n to oo)((1)/(n^2)+(2)/(n^2)+(3)/(n^2)+"………."+(n)/(n^2))` is

A

`1//4`

B

`1//6`

C

`1//9`

D

`1//12`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=lim_(nto oo)( 1/n)(x+1/n)^(2)+(x+2/n)^(2)+………+(x+(n-1)/n)^(2)`
`=int_(0)^(1)(x+y)^(2)dy`
`=x^(2)+x+1/3`
`:. f(x)=(x+1/2)^(2)+1/3-1/4`
`:.f(x)|_("min")=1/12`
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Knowledge Check

  • lim_(n rarr oo)((1)/(n^(2)) + (2)/(n^(2)) + (3)/(n^(2)) + …. + (n)/(n^(2))) is

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  • lim_(n to infty)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))+ . . . . +(n)/(n^(2))) is . . . . . . .

    A
    `(1)/(2)`
    B
    0
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