Home
Class 11
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` is equal to

A

`(n(n+1)(n+2))/6`

B

`sum n^2`

C

`^nC_3`

D

`^(n + 2)C_3`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    PATHFINDER|Exercise QUESTION BANK|41 Videos

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

Similar Questions

Explore conceptually related problems

The value of sum_(i=1)^nsum_(j=1)^isum_(k=1)^j1=220 , then the value of n equals a. 11 b. 12 c. 10 d. 9

sum_(r=1)^nr^2-sum_(m=1)^nsum_(r=1)^mr is equal to

The value of sum_(i-1)^nsum_(j=1)^isum_(k=1)^j1=286 , then the value of n equals

Evaluate, sum_(i = 0)^iinfty sum_(j = 0)^infty sum_(k = 0)^infty 1/(3^i cdot 3^j cdot 3^k) ( i ne j ne k)

sum_(i=1)^(oo)sum_(j=1)^(oo)sum_(k=1)^(oo)(1)/(a^(i+j+k)) is equal to (where |a| gt 1 )

The value of sum_(r=1)^n(sum_(p=0)^(r-1) ^nC_r ^rC_p 2^p) is equal to (a) 4^(n)-3^(n)+1 (b) 4^(n)-3^(n)-1 (c) 4^(n)-3^(n)+2 (d) 4^(n)-3^(n)

The value of the expression .^47C_4 + sum_(j = 1)^5 .^(52 - j)C_3 is equal to

If (1+x)^n=sum_(r=0)^n .^nC_r x^r then sum_(r=m)^n .^rC_m is equal to

Let S_k=underset(nrarrinfty)limsum_(i=0)^n1/(k+1)^i. Then sum_(k=1)^nkS_k equals

If the value of lim_(n rarr oo)(n^(-3/2)) sum_(j=1)^(6n) sqrt(j) is equal to sqrt(N) , then the value of N/(12) is __________

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Suppose that F(n + 1) =(2F(n) + 1)/2 for n = 1,2,3,,,, and F(1) = 2. T...

    Text Solution

    |

  2. The series of natural number is divided into groups 1 , 2, 3, 4,.........

    Text Solution

    |

  3. sum(i = 1)^n sum(j = 1)^i sum(k = 1)^j 1 is equal to

    Text Solution

    |

  4. The sides of a right angle triangle from a G.P. the tangent of the sma...

    Text Solution

    |

  5. If the first & the (2n + 1)th terms of an A.P. , a G.P & an H.P. of po...

    Text Solution

    |

  6. If the arithmetic mean of two positive numbers a & b (a gt b) is twice...

    Text Solution

    |

  7. If Sn denotes the sum to n terms of the series (1 le n le 9) 1 + 22 + ...

    Text Solution

    |

  8. If a , b , c are in H.P. , then

    Text Solution

    |

  9. Let S1 , S2,,,,, be squares such that for each n ge 1 the length of a ...

    Text Solution

    |

  10. Given a sequence t1 , t2 ,..... if its possible to find a function f(r...

    Text Solution

    |

  11. Given a sequence t1 , t2 ,..... if its possible to find a function f(r...

    Text Solution

    |

  12. Let a1, a2 , a3,...., am be the arithmetic means between -2 and 1027 a...

    Text Solution

    |

  13. Let a1, a2 , a3,...., am be the arithmetic means between -2 and 1027 a...

    Text Solution

    |

  14. If A, G and H are respectively arithmetic , geometric and harmonic mea...

    Text Solution

    |

  15. If A, G and H are respectively arithmetic , geometric and harmonic mea...

    Text Solution

    |

  16. Let a1,a2 ,a3 ...... be an A.P. Prove that sum(n=1)^(2m)(-1)^(n-1)an^2...

    Text Solution

    |

  17. A three digit number whose consecutive digits from a G.P. If we subtra...

    Text Solution

    |

  18. If an denotes the coefficient of x^n in P(x) = (1 + x+ 2x^2 + 3x^3 +.....

    Text Solution

    |

  19. Two consecutive numbers from 1,2,3,.....,n are removed, then arithmeti...

    Text Solution

    |

  20. The value of xyz is 55 or 343/55 according as the sequence a, x, y, z,...

    Text Solution

    |