Home
Class 12
MATHS
If (1 + x)^(n) = C(0) + C(1) x + C(2) x...

If ` (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) +…+ C_(n) x^(n)` , find the values of the following .
`sum_(i=0)^(n) sum_(j=0)^(n) (C_(i) + C_(j))`

A

`2^(2n)`

B

`2^(n)`

C

`2n`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
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

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) +…+ C_(n) x^(n) , find the values of the following . sum_(i=0)^(n) sum_(j=0)^(n) (i+j) C_(i) C_(j)

If (1 + x)^(n) = C_(0) = C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , find the values of the following (sumsum)_(0leilt j le n)jC_(i)

If (1 + x)^(n) = C_(0) = C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , find the values of the following (sumsum)_(0leile jlen)(i +j)(C_(i)pmC_(j) )^(2)

If (1 + x)^(n) = C_(0) = C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , find the values of the following underset(0leile jlen)(sumsum)C_(i)C_(j)

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + …+ C_(n) x^(n) , find the sum of the series (C_(0))/(2) -(C_(1))/(6) + (C_(2))/(10) + (C_(3))/(14) -...+ (-1)^(n) (C_(n))/(4n+2) .

If (x + a_(1)) (x + a_(2)) (x + a_(3)) …(x + a_(n)) = x^(n) + S_(1) x^(n-1) + S_(2) x^(n-2) + …+ S_(n) where , S_(1) = sum_(i=0)^(n) a_(i), S_(2) = (sumsum)_(1lei lt j le n) a_(i) a_(j) , S_(3) (sumsumsum)_(1le i ltk le n) a_(i) a_(j) a_(k) and so on . If (1 + x)^(n) = C_(0) + C_(1) x + C_(2)x^(2) + ...+ C_(n) x^(n) the cefficient of x^(n) in the expansion of (x + C_(0))(x + C_(1)) (x + C_(2))...(x + C_(n)) is

If (1 + x)^(n) = C_(0) + C_(1) x C_(2) x^(2) +…+ C_(n) x^(n) , then the sum C_(0) + (C_(0)+C_(1))+…+(C_(0) +C_(1) +…+C_(n -1)) is equal to

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that C_(0)^(2) - C_(1)^(2) + C_(2)^(2) -…+ (-1)^(n) *C_(n)^(2)= 0 or (-1)^(n//2) * (n!)/((n//2)! (n//2)!) , according as n is odd or even Also , evaluate C_(0)^(2) - C_(1)^(2) + C_(2)^(2) - ...+ (-1)^(n) *C_(n)^(2) for n = 10 and n= 11 .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that C_(0) C_(n) - C_(1) C_(n-1) + C_(2) C_(n-2) - …+ (-1)^(n) C_(n) C_(0) = 0 or (-1)^(n//2) (n!)/((n//2)!(n//2)!) , according as n is odd or even .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) +… + C_(n) x^(n) , prove that C_(0) + 2C_(1) + 3C_(2) + …+ (n+1)C_(n) = (n+2)2^(n-1) .

VMC MODULES ENGLISH-BINOMIAL THEOREM-LEVEL 2
  1. The value of ((50),(0))((50),(1))+((50),(1))((50),(2)) + ...+ ((50),(...

    Text Solution

    |

  2. The value of sum(r=0)^(n) sum(p=0)^(r) ""^(n)C(r) . ""^(r)C(p) is...

    Text Solution

    |

  3. If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) +…+ C(n) x^(n) , find the...

    Text Solution

    |

  4. (1+x)=C(0)+C(1)x+….+C(n)x^(n) then the value of sumsum(0lerltslen)C(r)...

    Text Solution

    |

  5. If (1 + x)^(n) = C(0) = C(1) x + C(2) x^(2) + …+ C(n) x^(n) , find...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. 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

    |

  19. about to only mathematics

    Text Solution

    |

  20. 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

    |