Home
Class 11
MATHS
Prove that (1)/(n+1)=(.^(n)C(1))/(2)-(...

Prove that
`(1)/(n+1)=(.^(n)C_(1))/(2)-(2(.^(n)C_(2)))/(3)+(3(.^(n)C_(3)))/(4)-"...."+(-1)^(n+1) (n(.^(n)C_(n)))/(n+1)`.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

Similar Questions

Explore conceptually related problems

Prove that (.^(n)C_(1))/(2) + (.^(n)C_(3))/(4) + (.^(n)C_(5))/(6) + "…." = (2^(n) - 1)/(n+1) .

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

The value of (.^(n)C_(0))/(n)+(.^(n)C_(1))/(n+1)+(.^(n)C_(2))/(n+2)+"..."+(.^(n)C_(n))/(2n)

Prove that .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "…." + n xx .^(n)C_(n) = n2^(n-1) . Hence, prove that .^(n)C_(1).(.^(n)C_(2))^(2).(.^(n)C_(3))^(3)"......."(.^(n)C_(n))^(n) le ((2^(n))/(n+1))^(.^(n+1)C_(2)) AA n in N .

Prove that , .^(n)C_(r)+3.^(n)C_(r-1)+3.^(n)C_(r-2)+^(n)C_(r-3)=^(n+3)C_(r)

Evaluate .^(n)C_(0).^(n)C_(2)+.^(n)C_(1).^(n)C_(3)+.^(n)C_(2).^(n)C_(4)+"...."+.^(n)C_(n-2).^(n)C_(n) .

The value of the sum (.^(n)C_(1))^(2)+(.^(n)C_(2))^(2)+(.^(n)C_(3))^(2)+....+(.^(n)C_(n))^(2) is -

Prove that .^(n)C_(1) - (1+1/2) .^(n)C_(2) + (1+1/2+1/3) .^(n)C_(3) + "…" + (-1)^(n-1) (1+1/2+1/3 + "…." + 1/n) .^(n)C_(n) = 1/n

Prove that .^(n)C_(0) - .^(n)C_(1) + .^(n)C_(2) - .^(n)C_(3) + "……" + (-1)^(r) .^(n)C_(r) + "……" = (-1)^(r ) xx .^(n-1)C_(r ) .

Prove that if ngt7 then .^(n-1)C_(3)+.^(n-1)C_(4)gt^(n)C_(3)

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Show that the integer next above (sqrt(3)+1)^(2m) contains 2^(m+1), as...

    Text Solution

    |

  2. Prove that (1^2)/3""^n C1+(1^2+2^2)/5""^n C2+(1^1+2^2+3^2)/7""^n C3+.....

    Text Solution

    |

  3. Prove that (1)/(n+1)=(.^(n)C(1))/(2)-(2(.^(n)C(2)))/(3)+(3(.^(n)C(3)...

    Text Solution

    |

  4. Find the sum 2..^(10)C(0) + (2^(2))/(2).^(10)C(1) + (2^(3))/(3).^(1...

    Text Solution

    |

  5. If in the expansion of (2x+5)^(10) , the numerically greatest term in ...

    Text Solution

    |

  6. Find the value of (1)/(81^(n))-(10)/(81^(n)).^(2n)C(1) + (10^(2))/(8...

    Text Solution

    |

  7. Find the value of 5C3 + 4C2

    Text Solution

    |

  8. Find the sum .^1C0+^2C1+^3C2+....+^(n+1)Cn ,where Cr=^n Crdot

    Text Solution

    |

  9. If (1+x+x^(2) + "……" + x^(n))^(n) = a(0) + a(1)x+a(2)x^(2) + "….." a(n...

    Text Solution

    |

  10. If n gt 2, then prove that C(1)(a-1) - C(2) xx (a-2) + "….." + (-1)^(...

    Text Solution

    |

  11. Find the sum C0-C2+C4-C6+ ......... ,where Cr=^n Cr .

    Text Solution

    |

  12. If x+y=1, prove that sum(r=0)^n .^nCr x^r y^(n-r) = 1.

    Text Solution

    |

  13. Find the sum 3 C1 + 5C2

    Text Solution

    |

  14. Prove that (.^(n)C(1))/(2) + (.^(n)C(3))/(4) + (.^(n)C(5))/(6) + "…." ...

    Text Solution

    |

  15. If (1+x)^n=sum(r=0)^n^n Cr , show that C0+(C1)/2++(Cn)/(n+1)=(2^(n+1...

    Text Solution

    |

  16. If underset(r=0)overset(2n)suma(r) (x-2)^(r) = underset(r=0)overset(2n...

    Text Solution

    |

  17. 3^(2n+2)-8n-9 is divisible by

    Text Solution

    |

  18. Statement 1: The number of distinct terms in (1+x+x^2+x^3+x^4)^(1000) ...

    Text Solution

    |

  19. The product of 3rd and 8th term of a GP is 243. If its 4th term is 3. ...

    Text Solution

    |

  20. The value of "^30C0.^30C10+^30C1.^30C11+^30C2.^30C(12)+……+^30C(20) . ^...

    Text Solution

    |