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

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

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

    VK JAISWAL|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|19 Videos

  • SEQUENCE AND SERIES

    VK JAISWAL|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|17 Videos

  • QUADRATIC EQUATIONS

    VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|45 Videos

  • SOLUTION OF TRIANGLES

    VK JAISWAL|Exercise Exercise-5 : Subjective Type Problems|13 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 rarr oo) (1 ^ (2) + 2 ^ (2) + 3 ^ (3) + ......... + n ^ (2)) / (n ^ (3))

lim_(n to oo) (1^(2)+2^(2)+3^(2)+…+n^(2))/(n^(3)) is equal to

lim_ (n rarr oo) ((1) / (2) +1+ (3) / (2) + ... + (n) / (2)) / (25n ^ (2) + n + 3)

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

Evaluate: lim_(n rarr oo)((1^(2))/(n^(3))+(2^(2))/(n^(3))+(3^(2))/(n^(4))+...+(1)/(n))

lim_(n rarr oo)(3^(n+1)+2^(n+2))/(3^(n-1)+2^(n-2)) =

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

Find lim_ (n rarr oo) [(n ^ (3) +1) ^ ((1) / (2)) - n ^ ((3) / (2))] -: n ^ ((3) / ( 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)).

VK JAISWAL-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 numbers in A.P. Then half of the ...

    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 ( x 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. Three distinct non-zero real numbers form an A.P. and the squares of t...

    Text Solution

    |

  7. which term of an AP is zero -48,-46,-44.......?

    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 ^(2) + (1)/(3) y ^(3) + (1)/(...

    Text Solution

    |