Home
Class 12
MATHS
If sn=""^nC0+2*""^nC1+3*""^nC2+...+(n+1)...

If `s_n=""^nC_0+2*""^nC_1+3*""^nC_2+...+(n+1)*""^nC_n` then find `sum_(n=1)^oos_n`.

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

Prove that ""^nC_0+2*""^nC_1+3*""^nC_2+...+(n+1)""^nC_n=(n+2)2^(n-1)

Prove that ""^nC_0-2*""^nC_1+3*""^nC_2-...+(-1)""^n(n+1)""^nC_n=0

Prove that ""^nC_0+3*""^nC_1+5*""^nC_2+...+(2n+1)""^nC_n=(n+1)2^(n)

Prove that 2*""^nC_0+2^2*(""^nC_1)/2+2^3*(""^nC_2)/3+...2^(n+1)*(""^nC_n)/(n+1)=(3^(n+1)-1)/(n+1)

If s=a+(a+d)+(a+2d)+...+(a+nd) and S=a+(a+d) * ""^nC_1 + (a+2d) * ""^nC_2 + ...+(a+nd) * ""^nC_n then prove that (n+1)S=2^n*s .

If "^nC_5= ^nC_12 find n.

The value of ""^0C_0-^nC_1+^nC_2-....+ -1^(n^n)C_n is

If S_n=^nC_0.^nC_1+^nC_1.^nC_2+.....+^nC_(n-1).^nC_n and if S_(n+1)/S_n=15/4 , then the sum of all possible values of n is (A) 2 (B) 4 (C) 6 (D) 8

Show that : ""^nC_0*m-""^nC_1*(m-1)+""^nC_2*(m-2)-...+(-1)^n*""^nC_n*(m-n)=0

A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. Prove that ""^nC0+3*""^nC1+5*""^nC2+...+(2n+1)""^nCn=(n+1)2^(n)

    Text Solution

    |

  2. Prove that ""^nC0-2*""^nC1+3*""^nC2-...+(-1)""^n(n+1)""^nCn=0

    Text Solution

    |

  3. If sn=""^nC0+2*""^nC1+3*""^nC2+...+(n+1)*""^nCn then find sum(n=1)^oos...

    Text Solution

    |

  4. Find the sum :1*""^nC0+2*""^nC1+3*""^nC2+4*""^nC3+…, where n is an odd...

    Text Solution

    |

  5. Show that :""^nC0*m-""^nC1*(m-1)+""^nC2*(m-2)-...+(-1)^n*""^nCn*(m-n)=...

    Text Solution

    |

  6. Evaluate sum(r=1)^npr/r*"^nCr where pr denotes the sum of the first r ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |