Home
Class 12
MATHS
The value of underset(r=0)overset(20)sum...

The value of `underset(r=0)overset(20)sum(-1)^(r )(.^(50)C_(r))/(r+2)` is equal to

A

`(2^(2n+1)(2n^(2)+2n-1))/((2n+1)(2n+2))`

B

`(2^(2n+1)(2n^(2)-2n+1)-2)/((2n+1)(2n+2))`

C

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

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise NUMERICAL VALUE TYPE FOR JEE MAIN|14 Videos

  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise JEE Archive|56 Videos

  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise LEVEL 1|89 Videos

  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

Similar Questions

Explore conceptually related problems

The value of underset(r=0)overset(40)sumr.^(40)C_(r).^(30)C_(r) is

sum_(r=0)^(n)(""^(n)C_(r))/(r+2) is equal to :

underset(r=1)overset(n)(sum)r(.^(n)C_(r)-.^(n)C_(r-1)) is equal to

The value of sum_(r=0)^(20)(-1)^(r )(""^(50)C_(r))/(r+2) is equal to

Equation x^(n)-1=0,ngt1,ninN, has roots 1,a_(1),a_(2),...,a_(n),. The value of underset(r=2)overset(n)sum(1)/(2-a_(r)), is

If .^(47)C_(4)+underset(r=1)overset(5)(sum).^(52-r)C_(3) is equal to

sum_(r=0)^n(-2)^r*(nC_r)/((r+2)C_r) is equal to

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

let underset(r=0)overset(2010)(sum)a_(r)x^(r)=(1+x+x^(2)+x^(3)+x^(4)+x^(5))^(402) and underset(r=0)overset(2010)(sum)a_(r)=a, then the value of ((underset(r=0)overset(2010)(sum)r.a_(r))/(underset(r=0)overset(2010)(sum)a_(r))) is equal to____.

The value of sum_(r=0)^(50)(-1)^r((50)C_r)/(r+2) is equal to a . 1/(50xx51) b. 1/(52xx50) c. 1/(52xx51) d. none of these

VMC MODULES ENGLISH-BINOMIAL THEOREM-LEVEL 2
  1. If (1 + x)^(n) = C(0) = C(1) x + C(2) x^(2) + …+ C(n) x^(n) , find...

    Text Solution

    |

  2. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+….+C(n)x^(n), then the value of sums...

    Text Solution

    |

  3. Prove that sum(r=0)^ssum(s=1)^n^n Cs^n Cr=3^n-1.

    Text Solution

    |

  4. The value of underset(r=0)overset(20)sum(-1)^(r )(.^(50)C(r))/(r+2) is...

    Text Solution

    |

  5. The value of ""^(n)C(n)+""^(n+1)C(n)+""^(n+2)C(n)+….+""^(n+k)C(n) :

    Text Solution

    |

  6. The value of sum(r=0)^50 (.^(100)Cr.^(200)C(150+r)) is equal to

    Text Solution

    |

  7. The value of sum(r=0)^(2n)(-1)^(r)*(""^(2n)C(r))^(2) is equal to :

    Text Solution

    |

  8. Find the sum sum(i=0)^r.^(n1)C(r-i) .^(n2)Ci .

    Text Solution

    |

  9. If a(n) = sum(r=0)^(n) (1)/(""^(n)C(r)) , find the value of sum(...

    Text Solution

    |

  10. sum(r=0)^n (-1)^r .^nCr (1+rln10)/(1+ln10^n)^r

    Text Solution

    |

  11. If R = (sqrt(2) + 1)^(2n+1) and f = R - [R], where [ ] denote the ...

    Text Solution

    |

  12. Let ( 5 + 2 sqrt(6))^(n) = I + f , where n, I in N and 0 lt f lt ...

    Text Solution

    |

  13. If x= (7 + 4 sqrt(3))^(2n) = [x] + f , where n in N and 0 le f lt...

    Text Solution

    |

  14. If n gt 3, then xyz^(n)C(0)-(x-1)(y-1)(z-1)""^(n)C(1)+(x-2)(y-2)(z-2)"...

    Text Solution

    |

  15. about to only mathematics

    Text Solution

    |

  16. If n gt 3, then xyz^(n)C(0)-(x-1)(y-1)(z-1)""^(n)C(1)+(x-2)(y-2)(z-2)"...

    Text Solution

    |

  17. Let n be positive integer such that, (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^...

    Text Solution

    |

  18. Find the value of underset(0leiltjlen)(sumsum)(.^(n)C(i)+.^(n)C(j)).

    Text Solution

    |

  19. If (1+x+x^(2))^(n) = a(0) + a(1)x+ a(2)x^(2) + "……" a(2n)x^(2n), find...

    Text Solution

    |

  20. Find the value of 1/(81^n)-(10)/(81^n)^(2n)C1+(10^2)/(81^n)^(2n)C2-(10...

    Text Solution

    |