Home
Class 12
MATHS
Evaluate: ("lim")(n to oo)((1^2+2^2+3^3+...

Evaluate: `("lim")_(n to oo)((1^2+2^2+3^3++n^2)(1^3+2^3+3^3++n^3))/(1^6+2^6+3^6++n^6)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

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_(n->oo)(1^2+2^2+3^2+..........+n^2)/n^3

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

Evaluate lim_(ntooo) (1^(3)+2^(3)+3^(3)+...+n^(3))/(sqrt(4n^(8)+1)).

The value of ("lim")_(n->oo)[(n+1)^2 3-(n-1)^2 3] is_____

(lim)_(n->oo)(1^2+2^2+3^2++n^2)/(n^3) is equal to a. 1 b . c. 1/3 d. 0

The value of lim_(nto oo)(1^(3)+2^(3)+3^(3)+……..+n^(3))/((n^(2)+1)^(2))

Evaluate : lim_(n-> oo) (1^4+2^4+3^4+...+n^4)/n^5 - lim_(n->oo) (1^3+2^3+...+n^3)/n^5

lim_(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /n^2)......(1+n^2 / n^2)]^(1/n)

Evaluate the following limit: (lim)_(n->oo)(1^3+2^3+ n^3)/((n-1)^4)

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Evaluate: inta^b cos x dx

    Text Solution

    |

  2. Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in R....

    Text Solution

    |

  3. Evaluate: ("lim")(n to oo)((1^2+2^2+3^3++n^2)(1^3+2^3+3^3++n^3))/(1^6+...

    Text Solution

    |

  4. ifint(dx)/(x^2(x^n+1)^(((n-1)/n))=-[f(x)]^(1/n)+c ,t h e nf(x)i s (1+...

    Text Solution

    |

  5. Evaluate the definite integrals as limit of sums int1^2x^2dx

    Text Solution

    |

  6. Evaluate: inta^bsinx dx using limit of sum

    Text Solution

    |

  7. int(-3)^3 x^8{x^11}dx

    Text Solution

    |

  8. Evaluate: inta^b e^x dx using limit of sum

    Text Solution

    |

  9. The value of int(-2)^1[x[1+cos((pix)/2)]+1]dx , where [.] denotes the...

    Text Solution

    |

  10. Evaluate: lim(n->oo)(((n+1)(n+2)...(n+n))^(1/n))/n

    Text Solution

    |

  11. If g(x)=int0^x(|sint|+|cost|)dt ,then g(x+(pin)/2) is equal to, where...

    Text Solution

    |

  12. Evaluate: lim(n->oo)[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

    Text Solution

    |

  13. int0^x|sint|dt, where x in (2npi,(2n+1)pi),ninN,is equal to (A) 4n...

    Text Solution

    |

  14. Evaluate lim(n->oo)n[1/((n+1)(n+2))+1/((n+2)(n+4))+....+1/(6n^2)]

    Text Solution

    |

  15. Let f(x) be an odd continous function which is periodic with period 2....

    Text Solution

    |

  16. Evaluate inta^b(dx)/(sqrt(x)),w h e r ea , b > 0.

    Text Solution

    |

  17. Let f: Rveca n dg: RvecR be continuous function. Then the value of the...

    Text Solution

    |

  18. Evaluate: int(-(3pi)/2)^(-pi/2)[(x+pi)^3+cos^2(x+3pi)]dx

    Text Solution

    |

  19. Evaluate: int0^(1/2)(xsin^(-1)x)/(sqrt(1-x^2))dx

    Text Solution

    |

  20. Evaluate: int0^(100)x-[x]dx where [dot] represents the greatest in...

    Text Solution

    |