Home
Class 11
MATHS
Let (1 + x)^n= C0+C1x+C2x^2+.....+Cn x^n...

Let `(1 + x)^n= C_0+C_1x+C_2x^2+.....+C_n x^n` and `C_1/C_0+2 C_2/C_1+3 C_3/C_2+.....+ n C_n/C_(n-1)= (n(n+1))/k`. The value of k is:

A

`1/2`

B

2

C

`1/3`

D

3

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    MODERN PUBLICATION|Exercise EXERCISE|221 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos

Similar Questions

Explore conceptually related problems

C_1/C_0+2C_2/C_1+3C_3/C_2+............+nC_n/C_(n-1)=(n(n+1))/2

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove the following : (1+C_1/C_0)(1+C_2/C_1)(1+C_3/C_2).... (1+C_n/ C_(n-1))=((n+1)^n)/(n!) .

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove that : C_0+ C_1/2 +C_2/3+.........+C_n/(n+1)= (2^(n+1)-1)/(n+1) .

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove that : C_0+ 2C_1 +.........+2""^nC_n=3^n .

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove the following : C_0-C_1/2+C_2/3-.....+(-1)^n C_n/(n+1)= 1/(n+1) .

If (1 + x)^n= C_0+C_1x+C_2x^2+.............+ C_n x^n , find the values of C_0^2+C_1^2+C_2^2+.....+C_n^2 .

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove the following : C_0-2C_1+3C_2-.........+(-1)^n (n+1)C_n=0 .

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove the following : C_0+1/3 C_2+1/5C_4+1/7C_6+.......... = 2^n/(n+1) .

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove the following : C_0C_n+C_1C_(n-1)+C_2C_(n-2)+.....+ C_nC_0= ((2n!))/(n!)^2 .

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove the following : 2C_0+2^2 C_1/2+2^3 C_2/3+........+2^(n+1) C_n/ (n+1)= (3^(n+1)-1)/(n+1) .

MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE
  1. In a binomial expansion (1 + x)^n is a positive integer, the coefficie...

    Text Solution

    |

  2. If the three consecutive coefficients in the expansion of (1 + x)^n ar...

    Text Solution

    |

  3. Let (1 + x)^n= C0+C1x+C2x^2+.....+Cn x^n and C1/C0+2 C2/C1+3 C3/C2+......

    Text Solution

    |

  4. In the expansion of (x +a)^n, the sums of the odd and the even terms a...

    Text Solution

    |

  5. The 5th term from the end in the expansion of (x^3/2-2/x)^12 is :

    Text Solution

    |

  6. In the binomial expansion of (a -b)^n, nge5, the sum of the 5th and 6t...

    Text Solution

    |

  7. The value of C (47, 4) + underset (r=1) overset (5) sum (52-r,3) is:

    Text Solution

    |

  8. 7^9+9^7 is divisible by :

    Text Solution

    |

  9. Find the term independent of x in the expansion of : ((x+1)/(x^(2//3)-...

    Text Solution

    |

  10. Product of any r consecutive natural numbers is always divisible by :

    Text Solution

    |

  11. If C0,C1,C2,........, Cn denote the coefficients in the expansion of (...

    Text Solution

    |

  12. A polygon has 44 diagonals. The number of the sides is :

    Text Solution

    |

  13. Find 'a' if the coefficients of x^(2) and x^(3) in the expanion of (3 ...

    Text Solution

    |

  14. Using binomial theorem. the value of (0.999)^3,correct to 3 decimal pl...

    Text Solution

    |

  15. The coefficient of x^n, where n is any positive integer, in the expans...

    Text Solution

    |

  16. If ""^(2n+1)P(n-1): ""^(2n-1)Pn =3:5 then the value of n equals :

    Text Solution

    |

  17. If|x|<1, then the coefficient of x^6 in the expansion of (1+x + x^2)^-...

    Text Solution

    |

  18. ""^15C0.""^5C5+""^15C1.""^5C4+""^15C2.""^5C3+ ""^15C3.^5C2+""^15C4.""^...

    Text Solution

    |

  19. Every body in a room shakes hand with every body else. The total numbe...

    Text Solution

    |

  20. ""^15C8+""^15C9-""^15C6-""^15C7=

    Text Solution

    |