Home
Class 11
MATHS
The value of ^n C1+^(n+1)C2+^(n+2)C3++^(...

The value of `^n C_1+^(n+1)C_2+^(n+2)C_3++^(n+m-1)C_m` is equal to

Text Solution

AI Generated Solution

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

The value of |1 1 1^n C_1^(n+2)C_1^(n+4)C_1^n C_2^(n+2)C_2^(n+4)C_2| is

The value of |[1, 1 ,1],[\ ^n C_1,\ ^(n+2)C_1,\ ^(n+4)C_1],[\ ^n C_2,\ ^(n+2)C_2,\ ^(n+4)C_2]| is (a) 2 (b) 4 (c) 8 (d) n^2

If (1+x)^n=C_0+C_1x+C_2x^2+...+C_nx^n then the value of (C_0)^2+(C_1)^2/2+(C_2)^2/3+...+(C_n)^2/(n+1) is equal to

The value of sum_(r=0)^(n-1)^n C_r//(^n C_r+^n C_(r+1)) equals a. n+1 b. n//2 c. n+2 d. none of these

If C_0, C_1, C_2,………C_n are binomial coefficients int eh expansion of (1+x)^n then and n is even, then C_0^2-C_1^2+C_2^2-C_3^2 + ... +(-1) C_n^2 , is equal to

The value of ""^(n)C_(n)+""^(n+1)C_(n)+""^(n+2)C_(n)+….+""^(n+k)C_(n) :

If the value of (n + 2) . ""^(n)C_(0) *2^(n+1) - (n+1) * ""^(n)C_(1)*2^(n) + n* ""^(n)C_(2) * 2^(n-1) -... is equal to k(n +1) , the value of k is .

If C_(0),C_(1),C_(2),C_(3), . . .,C_(n) be binomial coefficients in the expansion of (1+x)^(n) , then Q. The value of the expression C_(0)+2C_(1) +3C_(2)+. . . .+(n+1)C_(n) is equal to

The value of ""(n)C_(1). X(1 - x )^(n-1) + 2 . ""^(n)C_(2) x^(2) (1 - x)^(n-2) + 3. ""^(n)C_(3) x^(3) (1 - x)^(n-3) + ….+ n ""^(n)C_(n) x^(n) , n in N is

The value of determinant |[ ^n C_(r-1), ^n C_r, (r+1)^(n+2)C_(r+1)],[ ^n C_r, ^n C_(r+1),(r+2)^(n+2)C_(r+2)],[ ^n C_(r+1), ^n C_(r+2), (r+3)^(n+2)C_(r+3)]| is n^2+n-2 b. 0 c. ^n+3C_(r+3) d. ^n C_(r-1)+^n C_r+^n C_(r+1)

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. If (1+x)^n=C0+C1x+C2x^2+...+Cn x^n , t h e n C0-(C0+C1)+(C0+C1+C2)-(C0...

    Text Solution

    |

  2. In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N,

    Text Solution

    |

  3. The value of ^n C1+^(n+1)C2+^(n+2)C3++^(n+m-1)Cm is equal to

    Text Solution

    |

  4. If (1+x)^n=C0+C1x+C2x2++Cn x^n , n in N ,t h e nC0-C1+C2-+(-1)^(n-1)C...

    Text Solution

    |

  5. The 10th term of (3-sqrt((17)/4+3sqrt(2)))^(20) is (a) a irrational nu...

    Text Solution

    |

  6. For the expansion (xsinp+x^(-1)cosp)^(10),(p in R), The greatest v...

    Text Solution

    |

  7. Let (1+x^2)^2(1+x)^n=sum(k=0)^(n+4)ak x^k. If a1, a2 and a3 are in ari...

    Text Solution

    |

  8. The middle term in the expansion of (x//2+2)^8 is 1120, then x in R i...

    Text Solution

    |

  9. If (1+2x+x^2)^n=sum(r=0)^(2n)ar x^r ,then ar is a.(.^nC2)^2 b. .^n ...

    Text Solution

    |

  10. [(^nC0+^n C3+)-1/2(^n C1+^n C2+^n C4+^n C5]^2 + 3/4(^n C1-^n C2+^n C4 ...

    Text Solution

    |

  11. If sum(r=0)^(n)((r+2)/(r+1)).^n Cr=(2^8-1)/6 , then n is (A) 8 (B...

    Text Solution

    |

  12. Let f(x)=a0+a1x+a2x^2+...+an x^n and (f(x))/(1-x)=b0+b1x+b2x^2+...+bn ...

    Text Solution

    |

  13. If (1+x^(2))^(n) = underset(r=0)overset(n)suma(r)x^(r )= (1+x+x^(2)+x^...

    Text Solution

    |

  14. The value of sum(r=1)^(n+1)(sum(k=1)^n "^k C(r-1))( where r ,k ,n in ...

    Text Solution

    |

  15. If (x^2+x+1)/(1-x)=a0+a1x+a2x^2+ ,t h e nsum(r=1)^(50)ar is equal to 1...

    Text Solution

    |

  16. Find dy/dt , if y = (1 - cost)/(1 + cost) is

    Text Solution

    |

  17. The coefficient of x^9 in the expansion of (1+x)(1+ x^2)(1+x^3)....(1...

    Text Solution

    |

  18. The coefficients of three consecutive terms of (1+x)^(n+5) are in the ...

    Text Solution

    |

  19. If (1-x)^(-n)=a0+a1x+a2x^2+...+ar x^r+ ,t h e na0+a1+a2+...+ar is equa...

    Text Solution

    |

  20. The value of sum(r=0)^(20)r(20-r)(.^(20) Cr)^2 is equal to a. 400^(...

    Text Solution

    |