Home
Class 12
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
`underset(r=1)overset(n+1)sum(underset(k=1)overset(n)sum.^(k)C_(r-1))= underset(r=1)overset(n+1)sum(underset(k=1)overset(n)sum(.^(k+1)C_(r)-.^(k)C_(r)))`
`= underset(r=1)overset(n+1)sum(.^(n+1)C_(r)+.^(1)C_(r))`
`= 2^(n+1) - 2`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|27 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Linked Comphrension|20 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 8.8|10 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise For problems 3 and 4|2 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

CENGAGE PUBLICATION-BINOMIAL THEOREM-Single Correct Answer
  1. The value of sum(r=0)^(10)(r)^(20)Cr is equal to 20(2^(18)+^(19)C(10))...

    Text Solution

    |

  2. [(. ^nC0+^n C3+)-1/2(.^n C1+^n C2+^n C4+^n C5]^2 + 3/4(.^n C1-^n C2+^n...

    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. The sum sumsum(0leilejle10) (""^(10)C(j))(""^(j)C(i-1)) is equal to

    Text Solution

    |

  5. The value of the sum ""^(1000)C(50) + ""^(999)C(49) +""^(998)C(48)+"…....

    Text Solution

    |

  6. If sum(r=0)^(n){a(r)(x-alpha+2)^(r)-b(r)(alpha-x-1)^(r)}=0, then

    Text Solution

    |

  7. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

    Text Solution

    |

  8. The value of sum(r=2)^(10) ""^(r)C(2).""^(10)C(r) is

    Text Solution

    |

  9. If .^(n+1)C(r+1):^n Cr:^(n-1)C(r-1)=11 :6:3, then n r= 20 b. 30 c. 40...

    Text Solution

    |

  10. If a, b and c are three consecutive coefficients terms in the expansio...

    Text Solution

    |

  11. Which term in the expansion of (2-3x)^(19) has algebraically the last ...

    Text Solution

    |

  12. The value of (.^(n)C(0))/(n)+(.^(n)C(1))/(n+1)+(.^(n)C(2))/(n+2)+"..."...

    Text Solution

    |

  13. The value of sum(r=1)^(n) (-1)^(r+1)(""^(n)C(r))/(r+1) is equal to

    Text Solution

    |

  14. If sum(r=0)^(n)((r+2)/(r+1)).^n Cr=(2^8-1)/6 , then n is (A) 8 (B...

    Text Solution

    |

  15. The value of underset(r=0)overset(3)sum.^(8)C(r)(.^(5)C(r+1)-.^(4)C(r)...

    Text Solution

    |

  16. Find underset(r=0) overset(10)sumr^ (10)C(r).3^(r).(-2)^(10-r)

    Text Solution

    |

  17. a. 15 b. -15 c. 0 d. 51

    Text Solution

    |

  18. If (1+x)^n=C0+C1x+C2x^2+...+Cn x^n , then C0C2+C1C3+C2C4+...+C(n-2)Cn=...

    Text Solution

    |

  19. Text Solution

    |

  20. The value of sum(r=0)^(40) r""^(40)C(r)""^(30)C(r) is (a) 40.^(69)C(29...

    Text Solution

    |