Home
Class 11
MATHS
Find the sum sumsum(0leiltjlen)"^nCi...

Find the sum `sumsum_(0leiltjlen)"^nC_i`

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

Find the sum (sumsum)_(0leiltjlen) ""^(n)C_(i) .

Find the sumsum_(0leiltjlen)1 .

Find the sum sumsum_(0lt=ilt=jlt=n)^n C_i^n C_j

Find the value of sumsum_(0leiltjlen) (""^(n)C_(i)+""^(n)C_(j)) .

Find the sum sumsum_(0lt=i < jlt=n-1)j^n C_idot

Find the sum sumsum_(i!=j)^n ^nC_i^n C_j

Find the value of (sumsum)_(0leiltjlen) (1+j)(""^(n)C_(i)+""^(n)C_(j)) .

Find the value of sumsum_(0leilejlt=n)c_i^n"" c_j^ndot

Find the following sums : (i) sumsum_(inej) ""^(n)C_(i).""^(n)C_(j) , (ii) sumsum_(0leiltjlen) ""^(n)C_(i).""^(n)C_(j) . (iii) sumsum_(0leiltjlen) ""^(n)C_(i).""^(n)C_(j) .

Find the value of sumsum_(0leilejlt=n)(i+j)(nC_i+n C_j)dot

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Find the sum sumsum(0leiltjlen) "^nCi"^nCj

    Text Solution

    |

  2. Prove that sum(r=0)^ssum(s=1)^n^n Cs^n Cr=3^n-1.

    Text Solution

    |

  3. Find the sum sumsum(0leiltjlen)"^nCi

    Text Solution

    |

  4. Find the coefficient of x^4 in the expansion of (x/2-3/x^2)^10.

    Text Solution

    |

  5. Find the term in(3sqrt(((a)/(sqrt(b))) + (sqrt((b)/ ^3sqrt(a))))^(21) ...

    Text Solution

    |

  6. Using the binomial theorem, evaluate (102)^5 .

    Text Solution

    |

  7. Find the 6th term in expansion of (2x^2-1//3x^2)^(10)dot

    Text Solution

    |

  8. Find a if the 7th and 18th terms of the expansion (2+a)^(50) are equal...

    Text Solution

    |

  9. Find n , if the ratio of the fifth term from the beginning to the ...

    Text Solution

    |

  10. Simplify: x^5+10 x^4a+40 x^3a^2+80 x^2a^3+80 x a^4+32 a^5dot

    Text Solution

    |

  11. Find the value of (18^3+7^3+3xx18xx7xx25) /(3^6+6xx243xx2+15xx18xx4+20...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |