Home
Class 12
MATHS
((1)/(2) . (2)/(2))/(1^(3))+((2)/(3) . (...

`((1)/(2) . (2)/(2))/(1^(3))+((2)/(3) . (3)/(2))/(1^(3)+2^(3)) +((3)/(2) . (4)/(2))/(1^(3)+2^(3)+3^(3))+.. `. . to ` n` terms

A

a.`(1)/(n+1)`

B

b.` (n)/(n+1)`

C

c.` (2)/(n+3)`

D

d.`(3)/(n+5)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|32 Videos

  • MATHEMATICAL REASONING

    HIMALAYA PUBLICATION|Exercise Question Bank|97 Videos

Similar Questions

Explore conceptually related problems

The sum of (1^(3))/(1)+(1^(3)+2^(3))/(1+2)+ (1^(3)+2^(3)+3^(3))/(1+2+3)+.. . upto 10 terms is

1+(1+2)/(2)+(1+2+3)/(3) +(1+2+3+4)/(4)+.. . to n terms =

(1)/(2 !)+(2)/(3 !)+(3)/(4 !)+.. .. to n terms =

1 . 2+2 . 3+3 . 4+.. .. to n terms =

((-1+i sqrt(3))/(2))^(3 n)+((-1-i sqrt(3))/(2))^(3 n)=

If A=[((2)/(3), 1,(5)/(3)),((1)/(3), (2)/(3), (4)/(3)),((7)/(3), 2, (2)/(3))] and B=[((2)/(5), (3)/(5), 1),((1)/(5), (2)/(5), (4)/(5)),((7)/(5),(6)/(5),(2)/(5))] , then compute 3A-5B .

If the sum of n terms of the series : (1)/( 1^(3)) +( 1+2)/( 1^(3) + 2^(3)) +(1+2+3)/(1^(3) + 2^(3) + 3^(3)) + "......." in S_(n) , then S_(n) exceeds 199 for all n greater than :

Simplify 2^((2)/(3)).2^((1)/(3))

Let S_(n) = ( 1)/( 1^(3)) + ( 1+2)/( 1^(3) + 2^(3)) +"...." + ( 1+ 2 + "...." + n)/(1^(3) +2^(3)"...."+n^(3)), n = 1,2,3,"....." , Then S_(n) is not greater than :

If 2^(3)+4^(3)+6^(3)+.. .+(2 n)^(3)=k n^(2)(n+1)^(2) then k=

HIMALAYA PUBLICATION-MATHEMATICAL INDUCTION AND SUMMATION OF SERIES-Question Bank
  1. 4^(3)+5^(3)+6^(3)+.. .+10^(3)=

    Text Solution

    |

  2. 3+5+7+ …..to n^(th) term is

    Text Solution

    |

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

    Text Solution

    |

  4. The 10^(th ) term of the series 3+13+29+51+79+.. ..

    Text Solution

    |

  5. Sum to 30 terms of 3+4+8+9+13+14+18+19+.. is

    Text Solution

    |

  6. The greatest positive integer, which divides (n+1)(n+2)(n+3)(n+4) for ...

    Text Solution

    |

  7. The sum of cubes of three successive natural numbers is divisible by

    Text Solution

    |

  8. Product of 4 consecutive natural numbers is divisible by

    Text Solution

    |

  9. 49^(n)+16 n-1 is divisible by

    Text Solution

    |

  10. If n is a positive integer, then n^(3)+2n is divisible

    Text Solution

    |

  11. If n in N then 3 . 5^(2 n+1)+2^(3 n+1) is divisible by

    Text Solution

    |

  12. If n is a +ve integer, 4^(n)-3 n-1 is divisible by

    Text Solution

    |

  13. The greatest positive integer, which divides (n+1)(n+2)(n+3)(n+4) for ...

    Text Solution

    |

  14. The sum to n terms of the series (1)/(sqrt(1)+sqrt(3))+(1)/(sqrt(3)+...

    Text Solution

    |

  15. The sum of n terms of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+ (7)/(1...

    Text Solution

    |

  16. If n is odd then the sum of n terms of the series 1^(2)-2^(2)+3^(2)-...

    Text Solution

    |

  17. If log a+log (a^(2)/b)+log (a^(3)/b^(2))+.. .. n terms =(n)/(2)(P log ...

    Text Solution

    |

  18. For a natural number n which one is the correct statement?

    Text Solution

    |

  19. Sum of the series 1+(3^(2))/(2 !)+(3^(4))/(4 !)+(3^(6))/(6 !)+.. . . t...

    Text Solution

    |

  20. 1+(1+2)/(2)+(1+2+3)/(3) +(1+2+3+4)/(4)+.. . to n terms =

    Text Solution

    |