Home
Class 11
MATHS
If sum(r=0)^(n)((r+2)/(r+1)).^n Cr=(2^8-...

If `sum_(r=0)^(n)((r+2)/(r+1)).^n C_r=(2^8-1)/6` , then `n` is (A) 8 (B) 4 (C) 6 (D) 5

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

sum_(r=0)^(n)((r+2)/(r+1))*""^(n)C_(r) is equal to :

sum_(r=0)^(n)((r+2)/(r+1))*""^(n)C_(r) is equal to :

If sum_(r=0)^(n) (pr+2).""^(n)C_(r)=(25)(64) where n, p in N , then (a) p=3 (b) p=4 (c) n=7 (d) n=6

If sum_(r=0)^(n){("^(n)C_(r-1))/('^(n)C_(r )+^(n)C_(r-1))}^(3)=(25)/(24) , then n is equal to (a) 3 (b) 4 (c) 5 (d) 6

If sum_(r=0)^(n-1)log_(2)((r+2)/(r+1)) =prod_(r=10)^(99)log_(r) (r+1), then 'n' is equal to (A) 4 (B) 3 (C) 5 (D) 6

Find the sum of sum_(r=1)^n(r^n C_r)/(^n C_(r-1) .

If C_r stands for .^nC_r and sum_(r=1)^n (r.C_r)/(C_(r-1)) =210 then n= (A) 19 (B) 20 (C) 21 (D) none of these

If sum_(r=1)^n t_r= (n(n+1)(n+2))/3 then sum _(r=1)^oo 1/t_r= (A) -1 (B) 1 (C) 0 (D) none of these

The value of sum_(r=1)^(n)(-1)^(r-1)((r )/(r+1))*^(n)C_(r ) is (a) 1/(n+1) (b) 1/n (c) 1/(n-1) (d) 0

Prove that sum_(r=0)^(2n)(r. ^(2n)C_r)^2=n^(4n)C_(2n) .

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. If (1+2x+x^2)^n=sum(r=0)^(2n)ar x^r ,then ar is a.(.^nC2)^2 b. .^n ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. The coefficient of x^(10) in the expansion of (1+x^2-x^3)^8 is 476 b. ...

    Text Solution

    |

  14. If the term independent of x in the (sqrt(x)-k/(x^2))^(10) is 405, the...

    Text Solution

    |

  15. The coefficient of x^2y^3 in the expansion of (1-x+y)^(20) is (20 !)/(...

    Text Solution

    |

  16. The coefficient of x^5 in the expansion of (x^2-x-2)^5 is -83 b. -82 c...

    Text Solution

    |

  17. The coefficient of a^8b^4c^9d^9 in (a b c+a b d+a c d+b c d)^(10) is...

    Text Solution

    |

  18. If the coefficient of x^7in[a x^2-(1/(b x^2))]^(11) equal the coeffici...

    Text Solution

    |

  19. If (1+x)^5=a0+a1x+a2x^2+a3x^3+a4x^4+a5x^5, then the value of (a0-a2+a4...

    Text Solution

    |

  20. The coefficient of x^n in the expansion of (1+x)(1-x)^n is

    Text Solution

    |