Home
Class 11
MATHS
Prove that: sum(r=0)^(n) 3^( r) ""^(n)C(...

Prove that: `sum_(r=0)^(n) 3^( r) ""^(n)C_(r) = 4^(n)`.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    JBD PUBLICATION|Exercise EXAMPLE|36 Videos

Similar Questions

Explore conceptually related problems

Prove that sum_(r=0)^n 3^r "^nC_r= 4^n .

Statement-1: sum_(r =0)^(n) (r +1)""^(n)C_(r) = (n +2) 2^(n-1) Statement -2: sum_(r =0)^(n) (r+1) ""^(n)C_(r) x^(r) = (1 + x)^(n) + nx (1 + x)^(n-1)

The vaule of sum_(r=0)^(n-1) (""^(C_(r))/(""^(n)C_(r) + ""^(n)C_(r +1))) is equal to

Prove that "^nC_r+2 ^(n)C_(r-1)+ ^(n)C_(r-2) = ^(n+2)C_r .

If a + b = k, when a, b gt o and S(k, n) = sum _(r=0)^(n) r^(2) (""^(n) C_(r) ) a^(r) cdot b^(n-r) , then

Prove by mathematical induction that sum_(r=0)^(n)r^(n)C_(r)=n.2^(n-1), forall n in N .

If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , find the value of sum_(r=0)^(n) (r)/(""^(n)C_(r))

Prove that underset (r=0) overset (n) sum 3^r ""^nC_r =4^n .

Prove that sum_(r=0)^n^n C_rsinr xcos(n-r)x=2^(n-1)sin(n x)dot

sum_(r=1)^(n) {sum_(r1=0)^(r-1) ""^(n)C_(r) ""^(r)C_(r_(1)) 2^(r1)} is equal to

JBD PUBLICATION-BINOMIAL THEOREM-EXAMPLE
  1. Find the 6th term in the expansion of (3x^2-1/3x)^8

    Text Solution

    |

  2. Prove that: sum(r=0)^(n) 3^( r) ""^(n)C(r) = 4^(n).

    Text Solution

    |

  3. Using Binomial Theorem, evaluate each of the following:(99)^5.

    Text Solution

    |

  4. Find an approximation of (0.99)^5 using the first three terms of its e...

    Text Solution

    |

  5. (a + b)^4 -(a -b)^4 ਪਤਾ ਕਰੋ ਅਤੇ ਇਸਦੀ ਵਰਤੋਂ ਕਰਕੇ (sqrt3+sqrt2)^4-(sqrt...

    Text Solution

    |

  6. Write the general term in the expansion of: (2x+1/x)^5.

    Text Solution

    |

  7. Write the general term in the expansion of (x^(2)-yx)^(12), x ne 0

    Text Solution

    |

  8. Find 3rd term in the expansion of (3x-y^3/6)^4.

    Text Solution

    |

  9. Find 5th term in the expansion of (2x^2-1/3x)^11.

    Text Solution

    |

  10. Find the rth term from the end in the expansion of (x+a)^n.

    Text Solution

    |

  11. Find the 4th term from the end in the expansion of ((4x)/5-5/(2x))^9

    Text Solution

    |

  12. Find a positive value of m for which the coefficient of x^2 in the exp...

    Text Solution

    |

  13. In the expansion of (1+x)^n, the coefficient of x^(p-1) and of x^(q-1)...

    Text Solution

    |

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

    Text Solution

    |

  15. Find the coefficient of a^-6 b^4 in the expansion of (1/a-(2b)/3)^10.

    Text Solution

    |

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

    Text Solution

    |

  17. Expand each of the following expressions: (2x-3)^6.

    Text Solution

    |

  18. Expand the following expressions, using Binomial Theorem: (1+2x+x^2)^3...

    Text Solution

    |

  19. Simplify (x+2y)^10+(x-2y)^10.

    Text Solution

    |

  20. ਮੁੱਲ ਪਤਾ ਕਰੋ:-(a^2+ sqrt(a^2-1))^4 + (a^2- sqrt(a^2-1))^4

    Text Solution

    |