Home
Class 12
MATHS
Evaluate sum(r=0)^n(r+1)^2*"^nCr...

Evaluate `sum_(r=0)^n(r+1)^2*"^nC_r`

Text Solution

AI Generated Solution

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

Evaluate sum_(r = 0)^(n) 3^r ""^nC_r

Evaluate sum_(r=1)^np_r/r*"^nC_r where p_r denotes the sum of the first r natural numbers.

Find sum_(r=0)^n(r+1)*"^nC_rx^r

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

Evaluate sum_(r = 1)^(n) ""^nC_r 2^r

Evaluate : sum_(r = 1)^(n) ""^(n)C_(r) 2^r

Find the sum sum_(r=0)^n(-1)^r*(""^nC_r)/(""^(r+3)C_r)

If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , find the value of sum_(r=0)^(n) (r)/(""^(n)C_(r))

A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. Evaluate sum(r=1)^npr/r*"^nCr where pr denotes the sum of the first r ...

    Text Solution

    |

  2. Prove by binomial expansion that sum(k=1)^nk^2*"^nCk=n(n+1)2^(n-2)

    Text Solution

    |

  3. Evaluate sum(r=0)^n(r+1)^2*"^nCr

    Text Solution

    |

  4. If (1+x)^n=C0+C1x+C2x^2+C3x^3+...+Cnx^n then prove that 2.C0+2^2C1/2+2...

    Text Solution

    |

  5. If (1+x)^n=C0+C1x+C2x^2+C3x^3+...+Cnx^n then prove that C0-1/2C1+1/3C2...

    Text Solution

    |

  6. Prove that 3*""^10C0+3^2*(""^10C1)/2+3^3*(""^10C2)/3+...3^11*(""^10C10...

    Text Solution

    |

  7. Prove that 2*""^nC0+2^2*(""^nC1)/2+2^3*(""^nC2)/3+...2^(n+1)*(""^nCn)/...

    Text Solution

    |

  8. Find the sum sum(k=0)^n("^nCk)/((k+1)(k+2))

    Text Solution

    |

  9. Find the sum sum(r=0)^n(-1)^r*(""^nCr)/(""^(r+3)Cr)

    Text Solution

    |

  10. Find the sum sum(k=1) (""^nC(2k-1))/(2k)

    Text Solution

    |

  11. Find the sum sum(k=0)^n ("^nCk)/(k+1)

    Text Solution

    |

  12. If (1+x)^n=sum(r=0)^n Crx^r then prove that sum(r=0)^n (Cr)/((r+1)2^(r...

    Text Solution

    |

  13. Find sum(r=0)^n(r+1)*"^nCrx^r

    Text Solution

    |

  14. Show that C0^2-C1^2+C2^2-C3^2+...........+(-1)^n Cn^2=0 or (-1)^(n/2)C...

    Text Solution

    |

  15. Prove that (""^(2n)C(0))^(2)-(""^(2n)C(1))^(2)+(""^(2n)C(2))^(2)-…+(""...

    Text Solution

    |

  16. Sum of the products of the binomial coefficients C0,C1,C2,......Cn ta...

    Text Solution

    |

  17. Find the sum ^20C10.^15C0+^20C9.^15C1+^20C8.^15C2+....+^20C0.^15C10

    Text Solution

    |

  18. Prove that sum(r=1)^k (-3)^(r-1) "^(3n)C(2r-1) =0 , where k=(3n)/2 and...

    Text Solution

    |

  19. If p+q=1, then show that sum(r=0)^n r^2^n Crp^r q^(n-r)=n p q+n^2p^2do...

    Text Solution

    |

  20. Use a combinatorial argument to prove that (C(n,1))^2+2(C(n,2))^2+3(C...

    Text Solution

    |