Home
Class 12
MATHS
If n is a positive integer and Ck = .^nC...

If `n` is a positive integer and `C_k = .^nC_k` then find the value of `sum_(k=1)^n k^3 * (C_k/C_(k-1))^2.`

Promotional Banner

Topper's Solved these Questions

  • Binomial Theorem for Positive Integrel Index

    A DAS GUPTA|Exercise Exercise|113 Videos
  • Application of dy/dx

    A DAS GUPTA|Exercise Exercise|45 Videos
  • Circles

    A DAS GUPTA|Exercise EXERCISE|122 Videos

Similar Questions

Explore conceptually related problems

If n is a positive integer and C_(k)=.^(n)C_(k) then find the value of sum_(k=1)^(n)k^(3)*((C_(k))/(C_(k-1)))^(2)

If n is a positive integer and C_(k)=""^(n)C_(k) , then the value of sum_(k=1)^(n)k^(3)((C_(k))/(C_(k-1)))^(2) is :

If n is a positive integer SC_(k)=^(n)C_(k), find the value of (sum_(k=1)^(n)(k^(3))/(n(n+1)^(2)*(n+2))((C_(k))/(C_(k)-1))^(2))^(-1)

If sum_(k=1)^(n)k=45, find the value of sum_(k=1)^(n)k^(3).

If sum_(k=1)^(n)k=210, find the value of sum_(k=1)^(n)k^(2).

Evaluate : sum_(k=1)^n (2^k+3^(k-1))

Find the sum sum_(k=0)^n ("^nC_k)/(k+1)

The value of sum_(r=1)^(n+1)(sum_(k=1)^(n)C(k,r-1))=

sum_(k =1)^(n) k(1 + 1/n)^(k -1) =

A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. If n is a positive integer and Ck = .^nCk then find the value of sum(k...

    Text Solution

    |

  2. Determine the constant term in the expansion of (1+x+x^2+x^3)^10

    Text Solution

    |

  3. If the fourth term in the expansion of (px+1/x)^n is 5/2, then (n,p)...

    Text Solution

    |

  4. Show that there wil be a term independent of x in the expansion of (x^...

    Text Solution

    |

  5. Find the term which does not contain irrational expression in the expa...

    Text Solution

    |

  6. If in any binomial expansion a, b, c and d be the 6th, 7th, 8th and 9t...

    Text Solution

    |

  7. The value of x in the expression (x+x^((log)(10)))^5 if third term in ...

    Text Solution

    |

  8. Prove that the coefficient of the middle term in the expansion of (1+x...

    Text Solution

    |

  9. In the expansion of (1 + x)^43 ,the co-efficients of (2r + 1)th and (r...

    Text Solution

    |

  10. Prove that in the expansion of (1+x)^(2n), the coefficient of x^n is d...

    Text Solution

    |

  11. The coefficient of 5th, 6th and 7th terms in the expansion of (1+x)^n ...

    Text Solution

    |

  12. Given positive integers r>1,n> 2, n being even and the coefficient of...

    Text Solution

    |

  13. If the coefficients of three consecutive terms in the expansion of (1 ...

    Text Solution

    |

  14. If a,b,c be the three consecutive coefficients in the expansion of a p...

    Text Solution

    |

  15. If a,b,c and d are any four consecutive coefficients in the expansi...

    Text Solution

    |

  16. If a,b,c and d are any four consecutive coefficients in the expansi...

    Text Solution

    |

  17. If the four consecutive coefficients in any binomial expansion be a, b...

    Text Solution

    |

  18. Let (1+x^2)^2*(1+x)^n=sum(k=0)^(n+4)ak*x^k If a1, a2 and a3 are iun ...

    Text Solution

    |

  19. If n be a positive integer then prove that the integral part P of (5+2...

    Text Solution

    |

  20. If (9+4sqrt5)^n=p+beta where n and p are positive integers and beta is...

    Text Solution

    |

  21. Integer just greater tehn (sqrt(3)+1)^(2n) is necessarily divisible by...

    Text Solution

    |