Home
Class 11
MATHS
Prove that underset(r=0)oversetnsum3^r^n...

Prove that `underset(r=0)oversetnsum3^r^nC_r=4^n`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    V PUBLICATION|Exercise QUESTION BANK|80 Videos

Similar Questions

Explore conceptually related problems

Prove that nC_r = nC_(n-r)

Prove that overset(n) underset(r=0)Sigma^(n)C_(r) sin rx cos (n-r)x=2^(n-1) sin (nx) .

What is the value of underset1oversetnsum3^n ?

Prove that ^"" nC_r=^nC_(n-r)

Prove that (""^nP_r)/(""^nC_r)=r!

V PUBLICATION-BINOMIAL THEORM-QUESTIONBANK
  1. Find(x+1)^6+(x-1)^6. Hence, or otherwise evaluate (sqrt2+1)^6+(sqrt2-1...

    Text Solution

    |

  2. Show that 9^(n+1)-8n-9 is divisible by 64.

    Text Solution

    |

  3. Prove that underset(r=0)oversetnsum3^r^nCr=4^n

    Text Solution

    |

  4. Find the value of 'a' if the 17^th term and 18^th term in the expansio...

    Text Solution

    |

  5. Show that the middle term in the (1+x)^2n expansion os is (1.3.5.....(...

    Text Solution

    |

  6. Find the coefficient of x^6y^3 in the expansion of (x+2y)^9

    Text Solution

    |

  7. The second, 'third and fourth terms in the binomial expansion (x+a)^n ...

    Text Solution

    |

  8. The coefficients of three consecutive terms in the expansion of. (1+a)...

    Text Solution

    |

  9. Find the coefficient of x^5 in (x+3)^8.

    Text Solution

    |

  10. Find the coefficient of a^5b^7 in the expansion of (a-2b)^12

    Text Solution

    |

  11. Find the general term in the expansion of (x^2-y)^6.

    Text Solution

    |

  12. Find the general term in the expansion of (x^2-yx)^12,x!=0

    Text Solution

    |

  13. Find the 4th term in the expansion of (x-2y)^12

    Text Solution

    |

  14. Find the 13^th term in the expansion of (9x-1/(3sqrtx))^18

    Text Solution

    |

  15. Find the middle term in the expansion of (3-(x^3)/6)^7.

    Text Solution

    |

  16. Find the middle term in the expansion of (x/3+9y)^10

    Text Solution

    |

  17. In the expansion of (1+a)^(m+n), prove that the coefficient of a^m and...

    Text Solution

    |

  18. The coefficients of the (r-1)^(th),r^(th) and (r+1)^(th) terms in the ...

    Text Solution

    |

  19. Prove that the coefficient of x^n in the expansion of (1+x)^(2n) is ...

    Text Solution

    |

  20. Find the positive value of m for which the coefficient of x^2 in the e...

    Text Solution

    |