Home
Class 11
MATHS
Prove that sum(r=1)^(m-1)(2r^2-r(m-2)+1)...

Prove that `sum_(r=1)^(m-1)(2r^2-r(m-2)+1)/((m-r)^m C_r)=m-1/mdot`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

Similar Questions

Explore conceptually related problems

Prove that sum_(r=1)^n(-1)^(r-1)(1+1/2+1/3++1/r)^n C_r=1/n .

Prove that sum_(r = 1)^(n+1) (2^(r +1) C_(r - 1) )/(r (r + 1)) = (3^(n+2) - 2n - 5)/((n+1)(n+2))

Prove that (3!)/(2(n+3))=sum_(r=0)^n(-1)^r((^n C_r)/(^(r+3)C_r))

Prove that sum_(r = 0)^n r^2 . C_r = n (n +1).2^(n-2)

If k a n d n are positive integers and s_k=1^k+2^k+3^k++n^k , then prove that sum_(r=1)^m^(m+1)C_r s_r=(n+1)^(m+1)-(n+1)dot

The value of sum_(r=1)^(49)(2r^(2) - 48r +1)/((50-r).""^(50)C_(r)) is "_____" .

Prove that sum_(r=0)^(2n) r.(""^(2n)C_(r))^(2)= 2.""^(4n-1)C_(2n-1) .

Prove that sum_(r=0)^n^n C_r(-1)^r[i^r+i^(2r)+i^(3r)+i^(4r)]=2^n+2^(n/2+1)cos(npi//4), where i=sqrt(-1)dot

Show that sum_(k=m)^n ^kC_r=^(n+1)C_(r+1)-^mC_(r+1)

Prove that sum_(r = 1)^n r^3 ((n_C_r)/(C_(r - 1)))^2 = (n (n + 1)^2 (n+2))/(12)

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. In the expansion of (1 + x)^(n) (1 + y)^(n) (1 + z)^(n) , the sum of t...

    Text Solution

    |

  2. Prove that ^100 C0^(100)C2+^(100)C2^(100)C4+^(100)C4^(100)C6++^(100)C(...

    Text Solution

    |

  3. Prove that sum(r=1)^(m-1)(2r^2-r(m-2)+1)/((m-r)^m Cr)=m-1/mdot

    Text Solution

    |

  4. Find the coefficients of x^(50) in the expression (1+x)^(1000)+2x(1+x)...

    Text Solution

    |

  5. If b1, b2 bn are the nth roots of unity, then prove that ^n C1dotb1+^n...

    Text Solution

    |

  6. If .^(n+1)C(r+1) :^n Cr :^(n-1)C(r-1)=11 :6:3, then n r=? a. 20 b. 30...

    Text Solution

    |

  7. If the last tem in the binomial expansion of (2^(1/3)-1/(sqrt(2)))^n i...

    Text Solution

    |

  8. Find the last two digits of the number (23)^(14)dot

    Text Solution

    |

  9. The value of x for which the sixth term in the expansion of [2^(log)2s...

    Text Solution

    |

  10. If the 6th term in the expansion of(1/(x^(8/3))+x^2(log)(10)x)^8 is 56...

    Text Solution

    |

  11. The total number of terms which are dependent on the value of x in the...

    Text Solution

    |

  12. In the expansion of (3^(-x//4)+3^(5x//4))^(n) the sum of binomial coe...

    Text Solution

    |

  13. If n is an integer between 0 and 21, then the minimum value of n!(21-...

    Text Solution

    |

  14. If R is remainder when 6^(83)+8^(83) is divided by 49, then the value ...

    Text Solution

    |

  15. Let aa n db be the coefficients of x^3 in (1+x+2x^2+3x^3)^4a n d(1+x+2...

    Text Solution

    |

  16. Let 1+sum(r=1)^(10)(3^r.^(10)Cr+r.^(10)Cr)=2^(10)(alpha. 4^5+beta) whe...

    Text Solution

    |

  17. Let a=3^(1//224)+1 and for all n ge 3, let f(n)=""^(n)C(0)a^(n-1)-""...

    Text Solution

    |

  18. If the constant term in the binomial expansion of (x^2-1/x)^n ,n in N...

    Text Solution

    |

  19. The largest value of x for which the fourth tem in the expansion (5^(...

    Text Solution

    |

  20. The number of values in set of values of r for which ^23 Cr+2.^(23)C(...

    Text Solution

    |