Home
Class 12
MATHS
If C(0), C(1), C(2),…, C(n) denote the b...

If `C_(0), C_(1), C_(2),…, C_(n)` denote the binomial
coefficients in the expansion of `(1 + x)^(n) ,` then `sum_(r=0)^(n)sum_(s=0)^(n)(C_(r) +C_(s))`

Text Solution

Verified by Experts

`sum_(i=0)^(n) sum_(j=0)^(n) ( C_(i)+ C_(j))= sum_(i-0)^(n) sum_(j=0)^(n) C_(i) + sum_(i=0)^(n) sum_(j=0)^(n) C_(j) `
`sum_(j=0)^(n) (sum_(i=0)^(n) C_(i)) + sum_(i=0)^(n) (sum_(j=0)^(n) C_(j))`
`sum_(j=0)^(n) (2^(n)) + sum_(i=0)^(n) (2^(n)) = (n+1) *2^(n) + (n+1) *2^(n)`
` = 2 (n+1)2^(n) = (n+1)2^(n+1)` .
Promotional Banner

Topper's Solved these Questions

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise JEE Type Solved Example : (Matching Type Questions )|2 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise For Session 1|8 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|23 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos

Similar Questions

Explore conceptually related problems

If C_(0), C_(1), C_(2), …, C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then sum_(0 ler )^(n)sum_(lt s len)^(n)C_(r)C_(s) =.

If C_(0),C_(1),C_(2),.........,C_(n) denote the binomial coefficients in the expansion of (1+1)^(n), then sum_(0<=r

If C_(0), C_(1), C_(2), …, C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then C_(0)""^(2) + 2 C_(1)""^(2) + 3C_(2)""^(2) + ...+ (n +1)C_(n)""^(2) =

If C_(0), C_(1), c_(2),...,C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then C_(0) + (C_(1))/(2) + C_(2)/(3) + ...+ (C_(n))/(n+1) or, sum_(r=0)^(n) (C_(r))/(r+ 1)

If C_(0), C_(1), C_(2),..., C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then . 1^(2). C_(1) - 2^(2) . C_(2)+ 3^(2). C_(3) -4^(2)C_(4) + ...+ (-1).""^(n-2)n^(2)C_(n)= .

If C_(o)C_(1),C_(2),......,C_(n) denote the binomial coefficients in the expansion of (1+x)^(n), then the value of sum_(r=0)^(n)(r+1)C_(r) is

If C_(0), C_(1), C_(2),...,C_(n) denote the binomial coefficients in the expansion of (1 + x)^n) , then xC_(0)-(x -1) C_(1)+(x-2)C_(2)-(x -3)C_(3)+...+(-1)^(n) (x -n) C_(n)=

If C_(0), C_(1), C_(2), ..., C_(n) denote the binomial cefficients in the expansion of (1 + x )^(n) , then a C_(0) + (a + b) C_(1) + (a + 2b) C_(2) + ...+ (a + nb)C_(n) = .

ARIHANT MATHS-BIONOMIAL THEOREM-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If C(0), C(1), C(2),…, C(n) denote the binomial coefficients in the...

    Text Solution

    |

  2. The value of (30 0)(30 10)-(30 1)(30 11)+(30 2)(30 12)++(30 20)(30 30)...

    Text Solution

    |

  3. If the coefficient of pth, (p+1)thand (p+2)th terms in the expansion ...

    Text Solution

    |

  4. If the coefficient of x^7 in (ax^2+1/(bx))^11 is equal to the coeffici...

    Text Solution

    |

  5. For natural numbers m ,n ,if(1-y)^m(1+y)^n=1+a1y+a2y^2+ ,a n da1=a2=10...

    Text Solution

    |

  6. In the binomial expansion of (a - b)^(n) , n ge 5 , the sum of the ...

    Text Solution

    |

  7. The sum of the series C 20()0-C 20()1+C 20()2-C 20()3+...-...+C 20()(1...

    Text Solution

    |

  8. Statement-1: sum(r =0)^(n) (r +1)""^(n)C(r) = (n +2) 2^(n-1) Stat...

    Text Solution

    |

  9. The remainder left out when 8^(2n)""(62)^(2n+1) is divided by 9 is (1)...

    Text Solution

    |

  10. For r= 0, 1,.....,10, let Ar,Br, and Crdenote, respectively, the coe...

    Text Solution

    |

  11. So, statement-1 is also true. Stetement-2 is a correct expanation fo...

    Text Solution

    |

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

    Text Solution

    |

  13. If n is a positive integer, then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is ...

    Text Solution

    |

  14. In the expansion of ((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x-x^(1/2)))^10 ...

    Text Solution

    |

  15. The coefficients of three consecutive terms of (1+x)^(n+5) are in the ...

    Text Solution

    |

  16. If the coefficients of x^(3) and x^(4) in the expansion of (1 + ax + b...

    Text Solution

    |

  17. Coefficient of x^(11) in the expansion of (1+x^2)(1+x^3)^7(1+x^4)^(12)...

    Text Solution

    |

  18. The sum of coefficients in integral powers of x in the binominal expan...

    Text Solution

    |

  19. The coefficient of x^9 in the expansion of (1+x)(16 x^2)(1+x^3)(1+x^(1...

    Text Solution

    |

  20. If the number of terms in the expansion of (1-2/x+4/(x^2))^n , x!=0, i...

    Text Solution

    |

  21. Let m be the smallest positive integer such that the coefficient of x^...

    Text Solution

    |