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)`

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

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

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

The value of lim_(n to oo) ((1^(2)+2^(2)+………+n^(2))(1^(3)+2^(3)+……….+n^(3))(1^(4)+2^(4)+…………n^(4)))/((1^(5)+2^(5)+…………+n^(5))^(2))) is equal to

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

Evaluate : lim_(xrarroo)(1+2+3+...+n)/n^2

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

The value of lim_(n to oo) sum_(r=1)^(n)(r^(2))/(r^(3)+n^(3)) is -

Evaluate : underset(n to oo) lim[((1+1^(2)/n^(2)))(1+(2^(2))/(n^(2)))(1+(3^(2))/(n^(2)))…(1+(n^(2))/(n^(2)))]^((1)/(n))

Evaluate : lim_(nrarroo)[(1+(1)/(n^(2)))^((2)/(n^(2)))(1+(2^(2))/n^(2))^((4)/(n^(2)))(1+(3^(2))/(n^(2)))^((6)/(n^(2)))...(1+(n^(2))/(n^(2)))^((2n)/(n^(2)))]

Evaluate: ("lim")_(n rarr oo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(sqrt(3n^2)))

CENGAGE PUBLICATION-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 be an odd continous function which is periodic with priod 2 if g...

    Text Solution

    |

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

    Text Solution

    |

  17. Let f: R to R and g: R to R be continuous function. Then the value of ...

    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

    |