Home
Class 12
MATHS
underset(nrarroo)lim[(n+1)/(n^(2)+1^(2))...

`underset(nrarroo)lim[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+(n+3)/(n^(2)+3^(2))+...+(1)/(n)]`

Text Solution

AI Generated Solution

To solve the limit \[ \lim_{n \to \infty} \left( \frac{n+1}{n^2 + 1^2} + \frac{n+2}{n^2 + 2^2} + \frac{n+3}{n^2 + 3^2} + \ldots + \frac{1}{n} \right), \] we will break it down step by step. ...
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Self practive problem|106 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 1|64 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos

Similar Questions

Explore conceptually related problems

underset(nrarroo)lim[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

lim_(n rarr oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2)) + (n)/(n^(2)+3^(2))+......+(1)/(5n)) is equal to :

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

lim_(n to oo ) {(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+ (n)/(n^(2)+n^(2))} is equal to

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

Evaluate lim _( x to oo) ((1^(2) )/(n ^(3) +1 ^(3))+(2 ^(2))/(n ^(3) +2 ^(3)) + (3 ^(2))/(n ^(3)+ 3 ^(3))+ .... + (4)/(9n)).

lim_(nrarroo) [(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+...+(1)/(8n)] is equal to

underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)/(n)]

The value of lim_(ntooo)[1/(n^(2)+1^(2))+2/(n^(2)+2^(2))+………….+n/(n^(2)+n^(2))] , is

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

RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -High Level Problem
  1. underset(nrarroo)lim[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+(n+3)/(n^...

    Text Solution

    |

  2. Evaluate int(0)^(pi)sqrt((cosx+cos2x+cos3x)^(2)+(sinx+sin2x+sin3x)^(...

    Text Solution

    |

  3. Let alpha & beta be distinct positive roots of the equation tanx = 2x,...

    Text Solution

    |

  4. Evaluate : lim(ararr(pi/2)^(-)) int(0)^(a)(cosx)ln(cosx)dx

    Text Solution

    |

  5. Find the value of a(0 lt a lt 1) for which the following definite inte...

    Text Solution

    |

  6. Find the Lim(nrarroo) ((""^(3n)C(n))/(""^(2n)C(n)))^(1/n) Where ""^(...

    Text Solution

    |

  7. int0^oof(a/x+x/a)*(lnx)/x d x=lna*int(a/x+x/a)*(dx)/x

    Text Solution

    |

  8. Evaluate Lim(n->oo)n^2 int(-1/n)^(1/n) (2006sinx+2007cosx) |x|dx

    Text Solution

    |

  9. Find f(x) if it satisfies the relation f(x) = e^(x) + int(0)^(1) (x...

    Text Solution

    |

  10. Evaluate the definite integral: int(-1/(sqrt(3)))^(1/(sqrt(3)))((x^4)/...

    Text Solution

    |

  11. about to only mathematics

    Text Solution

    |

  12. Prove that for any positive integer k ,(sin2k x)/(sinx)=2[cosx+cos3x+...

    Text Solution

    |

  13. If n gt 1. Evaluate int(0)^(oo)(dx)/((x+sqrt(1+x^(2)))^(n))

    Text Solution

    |

  14. Let f(x) be a continuous function AA xepsilonR, except at x=0, such th...

    Text Solution

    |

  15. Given that lim(nrarroo) sum(r=1)^(n) (log(e)(n^(2)+r^(2))-2log(e)n)/n ...

    Text Solution

    |

  16. Given that lim(x to 0)(int(0)^(x)(t^(2))/(sqrt(a+t))dt)/(bx-sinx) = 1,...

    Text Solution

    |

  17. Sketch the graph of cos^(-1)(4x^3-3x) and find the area enclosed betwe...

    Text Solution

    |

  18. Consider a square with vertices at (1, 1), (-1, 1), (-1, -1) and (1, -...

    Text Solution

    |

  19. Let [x] denotes the greatest integer function. Draw a rough sketch of ...

    Text Solution

    |

  20. Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x l...

    Text Solution

    |

  21. Find the area of region : {(x,y) : 0 le y le x^(2) + 1, 0 le y le x + ...

    Text Solution

    |