Home
Class 11
MATHS
The value of sum(r=1)^(n+1)(sum(k=1)^n^k...

The value of `sum_(r=1)^(n+1)(sum_(k=1)^n`^kC_(r-1))` (where `r, k, n in N`) is equal to

A

`2^(n+1)-2`

B

`2^(n+1)-1`

C

`2^(n+1)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    PATHFINDER|Exercise QUESTION BANK |266 Videos
  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

The value of sum_(r=1)^n (^nP_r)/(r!) is

The value of cot(sum_(n=1)^(23)cot^-1(1+sum_(k=1)^n2k)) is

The value of sum_(r=0)^(3n-1)(-1)^r .^(6n)C_(2r+1)3^r is

The value of sum_(r=1)^(n) (-1)^(r+1)(""^(n)C_(r))/(r+1) is equal to

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)

Find the value of sum_(r=1)^(n) (r)/(1+r^(2)+r^(4))

The value of sum_(n=1)^oo(-1)^(n+1)(n/(5^n)) equals

The value of lim_(n->oo)sum_(r=1)^(n)1/(5^n).^n C_r(sum_(t=0)^(r-1).^r C_t .3^t) is equal to

The value of lim_(n to oo)sum_(r=1)^(n)(1)/(n)e^((r)/(n)) is -

The value of cot {sum_(n=1)^(23)cot^(-1)""(1+sum_(k-1)^(n)2k)} is

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. The sixth term in the expansion of {2^(log2root(5)(9^(x-1)+7))+1/2^(1/...

    Text Solution

    |

  2. The value of sum(r=0)^(20)r(20-r)(^(20)Cr)^2 is equal to ?

    Text Solution

    |

  3. The value of sum(r=1)^(n+1)(sum(k=1)^n^kC(r-1)) (where r, k, n in N) i...

    Text Solution

    |

  4. sum(r=0)^(300)arx^r=(1+x+x^2+x^3)^(100). If a=sum(r=0)^(300)ar, then s...

    Text Solution

    |

  5. Coefficient of x^50 in (1+x)^(1000)+2x(1+x)^(999)+3x^2(1+x)^(998)+.......

    Text Solution

    |

  6. C0/2-C1/3+C2/4-C3/5+.... is equal to

    Text Solution

    |

  7. The coefficient of x^7 in the expansion of (1-x-x^2+x^3)^6 is

    Text Solution

    |

  8. Let (1+x^(2))^(2) (1+x)^(n) = underset(k = 0)overset(n+4)suma(k)x^(k)....

    Text Solution

    |

  9. Coefficient of x^n in the expansion of (1+x)^(2n) is

    Text Solution

    |

  10. If (1+x+x^2)^n=a0+a1x+...+a(2n)x^(2n) then

    Text Solution

    |

  11. The coefficients of x^7 in the expansion of (x^3+3x+3/x+1/x^3)^5 is

    Text Solution

    |

  12. 3^(2n+2)-8n-9 is divisible by

    Text Solution

    |

  13. If (x+1/x+x^2+1/x^2)^11=a0x^(-22)+a1x^(-21)+.....+a44x^(22), then a0+a...

    Text Solution

    |

  14. If (8+3sqrt7)^n=P+F, where P is an integer and F is a proper fraction,...

    Text Solution

    |

  15. Let n=3^(100), then for n

    Text Solution

    |

  16. Let an=(1000)^n/(n!) for n in N. Then an is greatest, when

    Text Solution

    |

  17. Which of the following is/are correct

    Text Solution

    |

  18. Answer the following question based on above passage: The coefficient...

    Text Solution

    |

  19. Answer the following question based on above passage: The coefficient...

    Text Solution

    |

  20. Let P=sum(r=1)^(50)(^(50+r)Cr(2r-1))/(^(50)Cr(50+r)), Q=sum(r=1)^(50)(...

    Text Solution

    |