Home
Class 12
MATHS
Evaluate the following (i) lim(n to o...

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`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|15 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|14 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

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

Evaluate the following limits : Lim_( n to oo) (1+2/n)^(2n)

lim_(n to oo)(1-2n^(2))/(5n^(2)-n+100)=

Evaluate the following limit: (lim)_(n->oo)(1/(n^2)+2/(n^2)+3/(n^2)++(n-1)/(n^2\ ))

lim_(n to oo) {(1)/(n)+(1)/(n+1)+(1)/(n+2)+...+(1)/(3n)}=

lim_(n to oo)(n!)/((n+1)!-n!)

lim_(nto oo) (1)/(n^(2))sum_(r=1)^(n) re^(r//n)=

lim_(n rarr oo)2^(1/n)

Evaluate the following limit: (lim)_(n->oo)2^(n-1)sin(a/(2^n))

ARIHANT MATHS ENGLISH-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Evaluate the following (i) lim(n to oo)((1)/(n^(2))+(2)/(n^(2))+(3)...

    Text Solution

    |

  2. Evaluate: int(-pi//2)^(pi//2)(x^2cosx)/(1+e^x)dx

    Text Solution

    |

  3. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

    Text Solution

    |

  4. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

    Text Solution

    |

  5. Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...

    Text Solution

    |

  6. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  7. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  8. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  9. Let f:RtoR be a function defined by f(x)={([x],xle2),(0,xgt2):} where ...

    Text Solution

    |

  10. If alpha=int0^1(e^(9x+3tan^((-1)x)))((12+9x^2)/(1+x^2))dxw h e r etan^...

    Text Solution

    |

  11. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

    Text Solution

    |

  12. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  13. Match the conditions/ expressions in Column I with statement in Column...

    Text Solution

    |

  14. Match List I with List II and select the correct answer using codes gi...

    Text Solution

    |

  15. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

    Text Solution

    |

  16. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  17. The valued of int(sqrt(In2))^(sqrt(In3)) (x sinx^(2))/(sinx^(2)+sin(In...

    Text Solution

    |

  18. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

    Text Solution

    |

  19. The value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(4))dx is (are)

    Text Solution

    |

  20. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

    Text Solution

    |

  21. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

    Text Solution

    |