Home
Class 11
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)` , prove that
` C_(0) + 3C_(1) + 5C_(2) + …+ (2n +1)C_(n) = (n+1)^(2)`

A

`2^(n)`

B

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

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM AND ITS APPLCIATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|103 Videos

  • CARTESIAN CO-ORDINATE SYSTEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|27 Videos

Similar Questions

Explore conceptually related problems

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) .

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 (1*2) C_(2) + (2*3) C_(3) + …+ {(n-1)*n} C_(n) = n(n-1) 2^(n-2) .

(1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - 2C_(1) + 3C_(2) - 4C_(3) + … + (-1)^(n) (n+1) C_(n) = 0

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

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

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

Prove that : C_(0)-3C_(1)+5C_(2)- ………..(-1)^n(2n+1)C_(n)=0

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

OBJECTIVE RD SHARMA ENGLISH-BINOMIAL THEOREM AND ITS APPLCIATIONS -Chapter Test
  1. The expression [x+(x^(3)-1)^((1)/(2))]^(5)+[x-(x^(3)-1)^((1)/(2))]^(...

    Text Solution

    |

  2. The coefficient of x^(53) in the expansion sum(m=0)^(100)^(100)Cm(x-3)...

    Text Solution

    |

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

    Text Solution

    |

  4. Find the numerically grates term in the expansion of 3-5x^(15)w h e nx...

    Text Solution

    |

  5. In the expansion of (1+x)^(50), find the sum of coefficients of odd po...

    Text Solution

    |

  6. Find the position of the term independent of x in the expansion of (sq...

    Text Solution

    |

  7. If the coefficients of x^(7) and x^(8) in the expansion of (2+x/3)^(n)...

    Text Solution

    |

  8. If the rth term in the expansion of (x/3-2/x^(2))^(10 contains x^(4), ...

    Text Solution

    |

  9. If the third in the expansion of [x + x^(logx)]^(6) is 10^(6) , th...

    Text Solution

    |

  10. the value of x , for which the 6th term in the expansions of[2^log2sqr...

    Text Solution

    |

  11. If the coefficients of (p+1)th and (P+3)th terms in the expansion of (...

    Text Solution

    |

  12. about to only mathematics

    Text Solution

    |

  13. The value of C(0)+3C(1)+5C(2)+7C(3)+….+(2n+1)C(n) is equal to :

    Text Solution

    |

  14. Find the following sum : (1)/(n!) + (1)/(2!(n-2)!) + (1)/(4!(n-4)!)+...

    Text Solution

    |

  15. The coefficient of x^(n) y^(n) in the expansion of [(1 + x)(1+y) (x...

    Text Solution

    |

  16. If (1 + x - 2 x^(2))^(6) = 1 + C(1) x + C(2) x^(2) + C(3) x^(3) + …+ C...

    Text Solution

    |

  17. Find the ratio of the coefficient of x^(15) to the term independent of...

    Text Solution

    |

  18. Find the number of terms in the expansion of (x+y+z)^(n).

    Text Solution

    |

  19. In the expansion of (1+x)^30 the sum of the coefficients of odd powers...

    Text Solution

    |

  20. In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N,

    Text Solution

    |