Home
Class 11
MATHS
If for n in N ,sum(k=0)^(2n)(-1)^k(^(2n...

If for `n in N ,sum_(k=0)^(2n)(-1)^k(^(2n)C_k)^2=A ,` then find the value of `sum_(k=0)^(2n)(-1)^k(k-2n)(^(2n)C_k)^2dot`

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

If sum_(n=0)^oo2cot^(-1) ((n^2+n-4)/2)=kpi then find the value of k

Evaluate : sum_(k=1)^n (2^k+3^(k-1))

Let f(n)= sum_(k=1)^(n) k^2 ^"(n )C_k)^ 2 then the value of f(5) equals

Find the sum_(k=1)^(oo) sum_(n=1)^(oo)k/(2^(n+k)) .

The sum S_(n)=sum_(k=0)^(n)(-1)^(k)*^(3n)C_(k) , where n=1,2,…. is

If n is a positive integer and C_(k)=""^(n)C_(k) , then the value of sum_(k=1)^(n)k^(3)((C_(k))/(C_(k-1)))^(2) is :

Given (1-x^(3))^(n)=sum_(k=0)^(n)a_(k)x^(k)(1-x)^(3n-2k) then the value of 3*a_(k-1)+a_(k) is (a) "^(n)C_(k)*3^(k) (b) "^(n+1)C_(k)*3^(k) (c) "^(n+1)C_(k)*3^(k-1) (d) "^(n)C_(k-1)*3^(k)

The value of lim_(n->oo) sum_(k=1)^n log(1+k/n)^(1/n) ,is

lim_(n rarr infty) sum_(k=1)^(n) (n)/(n^(2)+k^(2)x^(2)),x gt 0 is equal to

If f(n)=prod_(i=2)^(n-1)log_i(i+1) , the value of sum_(k=1)^100f(2^k) equals

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Find the value of (18^3+7^3+3xx18xx7xx25) /(3^6+6xx243xx2+15xx18xx4+20...

    Text Solution

    |

  2. Find the approximation of (0. 99)^5 using the first three terms of its...

    Text Solution

    |

  3. If for n in N ,sum(k=0)^(2n)(-1)^k(^(2n)Ck)^2=A , then find the value...

    Text Solution

    |

  4. There are two bags each of which contains n balls. A man has to sele...

    Text Solution

    |

  5. Find the sum sum(i=0)^r.^(n1)C(r-i) .^(n2)Ci .

    Text Solution

    |

  6. Prove that sum(r=0)^(2n)(r. ^(2n)Cr)^2=n^(4n)C(2n) .

    Text Solution

    |

  7. If k a n d n are positive integers and sk=1^k+2^k+3^k++n^k , then prov...

    Text Solution

    |

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

    Text Solution

    |

  9. Prove that (C1)/1-(C2)/2+(C3)/3-(C4)/4++((-1)^(n-1))/n Cn=1+1/2+1/3++1...

    Text Solution

    |

  10. Prove that sum(r=0)^n^n Crsinr xcos(n-r)x=2^(n-1)sin(n x)dot

    Text Solution

    |

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

    Text Solution

    |

  12. Find the last two digits of the number 27^(27)dot

    Text Solution

    |

  13. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

    Text Solution

    |

  14. Find the value of (sqrt(2)+1)^6-(sqrt(2)-1)^6dot

    Text Solution

    |

  15. Using binomial theorem (without using the formula for .^n Cr) , prove ...

    Text Solution

    |

  16. Prove that .(r+1)*^n Cr-r*^n Cr+ ... +(-1)^r.^n Cr=(-1)^r.^(n-2)Crdot

    Text Solution

    |

  17. Find the sum .^n C0+^n C4+^n C8 + . . .

    Text Solution

    |

  18. Find the value of ^4nC0+^(4n)C4+^(4n)C8++""^(4n)C(4n) .

    Text Solution

    |

  19. Find the coefficient of x^n in the polynomial (x+^n C0)(x+3^n C1)xx(x+...

    Text Solution

    |

  20. If (1+x)^(15)=C0+C1x+C2x^2++C(15)x^(15), then find the value of C2+2C...

    Text Solution

    |