Home
Class 12
MATHS
sum(i=1)^(n) sum(j=1)^(i)sum(k=1)^(j) 1 ...

`sum_(i=1)^(n) sum_(j=1)^(i)sum_(k=1)^(j) `1 equals `:`

A

`sum n`

B

`sum n^(2)`

C

`sum n^(3)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
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

If sum_(r=1)^(n) t_(r ) = sum_(k=1)^(n) sum_(j=1)^(k) sum_(i=1)^(j) 2 , then sum_(r=1)^(n) (1)/( t_(r )) equals :

The value of sum_(i=0)^oosum_(j=0)^oosum_(k=0)^oo1/(3^i3^j3^k) is

sum_(r=1)^(n)(sum_(p=0)^(r-1)""^(n)C_(r)""^(r)C_(p)2^(p)) is equal to:

If n is a positive integer and C_(k)=""^(n)C_(k) , then the value of sum_(k=1)^(n)k^(3)((C_(k))/(C_(k-1)))^(2) equals:

If sum_(i=1)^(2 n) cos ^(-1) x_(i)=0, then sum_(i=1)^(2 pi) x_(i)=

If the arithmetic mean of a_(1),a_(2),a_(3),"........"a_(n) is a and b_(1),b_(2),b_(3),"........"b_(n) have the arithmetic mean b and a_(i)+b_(i)=1 for i=1,2,3,"……."n, prove that sum_(i=1)^(n)(a_(i)-a)^(2)+sum_(i=1)^(n)a_(i)b_(i)=nab .

lim_(n to oo) 1/(n^2) sum_(r = 1)^(n) re^(r//n) equals :

If x+y=1 , then sum_(r=0)^(n)r^(2)""^(n)C_(r)x^(r)y^(n-r) equals:

If sum_(i=1)^(2n) sin^(-1) x_i=npi , then sum_(i=1)^(2n) x_i equals :

If sum_(i=1)^(2n) sin^(-1) x_i =npi , then sum_(i=1)^(2n) x_i is equal to :

HIMALAYA PUBLICATION-MATHEMATICAL INDUCTION AND SUMMATION OF SERIES-Question Bank
  1. Find the sum to n terms of the series 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)...

    Text Solution

    |

  2. If a(k)=(1)/(k(k+1)) for k=1,2,3, .., n, then (sum(k=1)^(n) a(k))^(...

    Text Solution

    |

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

    Text Solution

    |

  4. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

    Text Solution

    |

  5. If t(n)=(1)/(4)(n+2)(n+3) , n=1,2,3, .. then (1)/(t(1))+(1)/(t(2))...

    Text Solution

    |

  6. sum(k=1)^(5) (1^(3)+2^(3)+.. ..+k^(3))/(1+3+5+.. ..+(2 k-1))=

    Text Solution

    |

  7. For all integers n ge 1, which of the following is divisible by 9

    Text Solution

    |

  8. The sum of first n terms of the series 1^(2) + 2.2^(2) +3^(2) + 2. 4...

    Text Solution

    |

  9. If S(n)=(1)/(6.11)+(1)/(11.16)+(1)/(16.21)+ ….. to n terms, then 6S(n)...

    Text Solution

    |

  10. 1/(2*5)+1/(5*8)+1/(8*11)+............1/((3n-1)(3n+2))=n/((6n+4)) foral...

    Text Solution

    |

  11. Sum to n terms of the series (1)/(2 . 5) +(1)/(5 . 8)+(1)/(8 . 11)+..=

    Text Solution

    |

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

    Text Solution

    |

  13. The number (49^(2)-4)(49^(3)-49) is divisible by

    Text Solution

    |

  14. The sum of 1^(st) n terms of the series (1^(2))/(1) + (1^(2) + 2^(2...

    Text Solution

    |

  15. 1+3+5+7+..+29+30+31+32+..+60=

    Text Solution

    |

  16. The sum of n terms of the series 1+(1+3)+(1+3+5)+.. .. .. is

    Text Solution

    |

  17. 1+(3)/(2)+(5)/(2^(2))+(7)/(2^(3))+.. .. to infty=

    Text Solution

    |

  18. sum(i=1)^(n) sum(j=1)^(i)sum(k=1)^(j) 1 equals :

    Text Solution

    |

  19. The sum 1^(2)+1+2^(2)+2+3^(2)+3+..+n^(2)+n is

    Text Solution

    |

  20. The sum to infinity of the series : 1+ ( 2)/( 3) + ( 6)/( 3^(2)) +(...

    Text Solution

    |