Home
Class 12
MATHS
Let alpha =lim (x to oo) ((1 ^(3) -1 ^(2...

Let `alpha =lim _(x to oo) ((1 ^(3) -1 ^(2))+(2 ^(3) -2 ^(2))+...+ (n^(3) -n^(2)))/(n ^(4)),` then` alpha` is equal to:

A

`1/3`

B

`1/4`

C

`1/2`

D

non-exisitent

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|19 Videos
  • SEQUENCE AND SERIES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|16 Videos
  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|45 Videos
  • SOLUTION OF TRIANGLES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-5 : Subjective Type Problems|11 Videos

Similar Questions

Explore conceptually related problems

Let alpha=lim_(n->oo)((1^3-1^2)+(2^3-2^2)+.....+(n^3-n^2))/(n^4), then alpha is equal to :

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

lim _(x to oo) (1)/(n ^(3))(sqrt(n ^(2)+1)+2 sqrt(n ^(2) +2 ^(2))+ .... + n sqrt((n ^(2) + n ^(2)))=:

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)).

Let f(x)=lim_(n to oo) ((2 sin x)^(2n))/(3^(n)-(2 cos x)^(2n)), n in Z . Then

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

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

The value of lim_(n to oo)((1)/(1^(3)+n^(3))+(2^(2))/(2^(3)+n^(3))+..........+(n^(2))/(n^(3)+n^(3))) is :

lim_(n to oo){(1^(m)+2^(m)+3^(m)+...+ n^(m))/(n^(m+1))} equals

lim_(n to oo)((1)/(1+n^(3))+(4)/(8+n^(3))+....+(r^(2))/(r^(3)+n^(3))+....+(1)/(2*n^3)

VIKAS GUPTA (BLACK BOOK) ENGLISH-SEQUENCE AND SERIES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Let alpha =lim (x to oo) ((1 ^(3) -1 ^(2))+(2 ^(3) -2 ^(2))+...+ (n^(3...

    Text Solution

    |

  2. Let a,b,c,d be four distinct real number in A.P.Then the smallest posi...

    Text Solution

    |

  3. The sum of all digits of n for which sum (r =1) ^(n ) r 2 ^(r ) = 2+2^...

    Text Solution

    |

  4. If lim ( n to oo) (r +2)/(2 ^(r+1) r (r+1))=1/k, then k =

    Text Solution

    |

  5. The value of sum (r =1) ^(oo) (8r)/(4r ^(4) +1) is equal to :

    Text Solution

    |

  6. If three non-zero distinct real numbers form an arithmatic progression...

    Text Solution

    |

  7. The sum of the fourth and twelfth term of an arithmetic progression is...

    Text Solution

    |

  8. In an increasing sequence of four positive integers, the first 3 terms...

    Text Solution

    |

  9. The limit of (1)/(n ^(4)) sum (k =1) ^(n) k (k +2) (k +4) as n to oo i...

    Text Solution

    |

  10. Which is the last digit of 1+2+3+……+ n if the last digit of 1 ^(3) + ...

    Text Solution

    |

  11. There distinct positive numbers, a,b,c are in G.P. while log (c) a, lo...

    Text Solution

    |

  12. The numbers 1/3, 1/3 log (x) y, 1/3 log (y) z, 1/7 log (x) x are in H...

    Text Solution

    |

  13. If sum ( k =1) ^(oo) (k^(2))/(3 ^(k))=p/q, where p and q are relativel...

    Text Solution

    |

  14. The sum of the terms of an infinitely decreassing Geometric Progressio...

    Text Solution

    |

  15. A cricketer has to score 4500 runs. Let a (n) denotes the number of ru...

    Text Solution

    |

  16. If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...

    Text Solution

    |

  17. Let f (n)=(4n + sqrt(4n ^(2) -1))/( sqrt(2n +1 )+sqrt(2n-1)),n in N th...

    Text Solution

    |

  18. Find the sum of series 1+1/2+1/3+1/4+1/6+1/8+1/9+1/12+…… oo, where the...

    Text Solution

    |

  19. Let a (1), a(2), a(3),…….., a(n) be real numbers in arithmatic progres...

    Text Solution

    |

  20. Let the roots of the equation 24 x ^(3) -14x ^(2) + kx +3=0 form a geo...

    Text Solution

    |

  21. How many ordered pair (s) satisfy log (x ^(3) + (1)/(3) y ^(3) + (1)/(...

    Text Solution

    |