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

`lim_(n to oo) [ 1/(n^2) + 2/(n^2) + … + n/(n^2)]`

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The correct Answer is:
`1/2`
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Explore conceptually related problems

lim_(n to oo) [ 1^2/n^3 + (2^2)/(n^3) + …+ ((n-1)^2)/(n^3)]

Evaluate the following (i) lim_(n to oo)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))....+(n-1)/(n^(2))) (ii) lim_(n to oo)((1)/(n+1)+(1)/(n+2)+....+(1)/(2n)) (iii) lim_(n to oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+(n)/(2n^(2))) (iv) lim_(n to oo)((1^(p)+2^(p)+.....+n^(p)))/(n^(p+1)),pgt0

The value of lim_( n to oo) ((1)/(n) + (n)/((n+1)^2) + (n)/( (n+2)^2) + ...+ (n)/( (2n-1)^2) ) is

lim_(n to oo)[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+....+(1)/(n)]

lim_(n rarr oo)(n^(2))/(2^(n))

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

lim_ (n rarr oo) ((1) / (n ^ (2)) + (2) / (n ^ (2)) + (3) / (n ^ (2)) ++ (n-1) / (n ^ (2)))

MCGROW HILL PUBLICATION-DEFINITE INTEGRALS-Questions from Previous Years. B-Architecture Entrance Examination Papers
  1. lim(n to oo) [ 1/(n^2) + 2/(n^2) + … + n/(n^2)]

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  2. Evaluate int(-4)^(-5)e^((x+5^(2))) dx+3int(1//3)^(2//3)e^(9(x-(2)/(3))...

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  3. If f is continuously differentiable function then int(0)^(1.5) [x^2] f...

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  4. int(-a)^(a) log (x+ sqrt(x^(2) + 1 ) ) dx

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  5. If f(x) = (1)/( 2^n) when (1)/( 2^(n+1) ) lt x le (1)/( 2^n) , n= 0,...

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  6. The value of int(0)^(1) x^(2) (1- x)^(9) dx is

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  7. The value of int(0)^(1) "max" (e^(x) , e^(1-x) ) dx equals

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  8. int(0)^(pi//2) x sin cos x dx=?

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  9. Let f: R to R be defined by f(x) = int(0)^(1) (x^2 + t^2) /( 2-t) dt. ...

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  10. The equation of a curve is given by y= f(x), where f'(x) is a continuo...

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  11. Using the fact that 0 le f(x) le g(x) , c lt x lt d rArr int(c)^(d) f(...

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  12. lim(n to oo) (1)/(n) [ 1+ (n^2)/( n^2+ 1^2) + (n^2)/( n^2+ 2^2) + …+ ...

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  13. If f(x) = x [x], then for any real number a and b with a lt b, then va...

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  14. The integral int( sqrt(log 5) )^( sqrt(log 7 ) ) ( x cos x^(2) )/( cos...

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  15. If f(x)=(e^(2))/(1+e^(x)),I(1)=overset(f(a))underset(f(-a))int xg{x(1-...

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  16. The integral int(0)^(1//2) (e^(x) (2 -x ^2) )/( (1-x)^(3//2) (1+x)^(1/...

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  17. The integral I= int(0)^(2) [x^2] dx ([x] denotes the greatest integer ...

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  18. The integral int(pi//24)^(5pi//24) (dx)/( 1+ root(3)(tan 2x) ) is equa...

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  19. If f(x) = int(e)^(e^(x) ) log ((x)/( log t))dt, then the value of (3...

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