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

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

Text Solution

Verified by Experts

LHS=`.^(n)C_(0) xx 3^(0) + .^(n)C_(1) xx 3 + .^(n)C_(2) xx 3^(2)+...+^(n)C_(n)3^(n)`
`=(1+3)^(n)=4^(n)= RHS " "` [by binomial expansion].
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    RS AGGARWAL|Exercise EXERCISE 10B|16 Videos

  • BINOMIAL THEOREM

    RS AGGARWAL|Exercise EXERCISE 10B|16 Videos

  • ARITHMETIC PROGRESSION

    RS AGGARWAL|Exercise Exercise 11F (Very Short-Answer Type Questions)|17 Videos

  • CIRCLE

    RS AGGARWAL|Exercise EXERCISE 21 B|18 Videos

Similar Questions

Explore conceptually related problems

Prove that sum_(r=0)^(n)nC_(r)3^(r)=4^(n)

Prove that sum_(r=0)^(n)3^(rn)C_(r)=4^(n)

Prove that sum_(r=0)^(n)r(n-r)C_(r)^(2)=n^(2)(^(2n-2)C_(n))

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

Prove that sum_(r=0)^(n)C_(r)sin rx cos(n-r)x=2^(n-1)sin(nx)

If x+y=1, prove that sum_(r=0)^(n)nC_(r)x^(r)y^(n-r)

prove that sum_(r=0)^(n)3^(r)nC_(r)=4^(n)

RS AGGARWAL-BINOMIAL THEOREM-EXERCISE 10A
  1. Evalute: (2+sqrt(3))^(7)+(2-sqrt(3))^(7)

    Text Solution

    |

  2. Evalute: (sqrt(3)+sqrt(2))^(6)- (sqrt(3)-sqrt(2))^(6)

    Text Solution

    |

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

    Text Solution

    |

  4. Using binomial theorem, evaluate each of the following: (i)(104)^(4...

    Text Solution

    |

  5. Using binomial theorem, prove that (2^(3n)-7n-1) is divisible by 49, w...

    Text Solution

    |

  6. Prove that (2+sqrt(x))^(4)+(2-sqrt(x))^(4)= 2(16+24x+x^(2)).

    Text Solution

    |

  7. Find the 7th term in the expansion of ((4x)/5+5/(2x))^(8)

    Text Solution

    |

  8. Find the 9th term in the expansion of (a/b-b/(2a)^(2))^(12).

    Text Solution

    |

  9. Find the 16th term in the expansion of (sqrt(x)-sqrt(y))^(17)

    Text Solution

    |

  10. Find the 13^(t h)term in the expansion of (9x-1/(3sqrt(x)))^(18),x!=0

    Text Solution

    |

  11. If the coefficients of x^7 and x^8 in the expansion of [2 +x/3]^n a...

    Text Solution

    |

  12. The ratio of the coefficient of x^(15) to the term independent of x in...

    Text Solution

    |

  13. Prove that the ratio of the coefficient of x^10 in (1 - x^2)^10 & the ...

    Text Solution

    |

  14. Find the term independent of x in the expansion of (1+x+2x^3)[(3x^2//2...

    Text Solution

    |

  15. Find the coefficient of :\ x\ in the expansion of (1-3x+7x^2)(1-x)^(1...

    Text Solution

    |

  16. Find the coefficient of (i) x^(5)" in the expansion of "(x+3)^(8) (...

    Text Solution

    |

  17. Show that the term containing to does not exist in the expansion of (3...

    Text Solution

    |

  18. Does the expansion of (2x^2-1/x)^(20) contain any term involving x^9?

    Text Solution

    |

  19. Show that the expansion of (x^2+1/x)^1 does not contain any term invol...

    Text Solution

    |

  20. Write the general term in the expansion of (x^(2)-y)^(6).

    Text Solution

    |