Home
Class 12
MATHS
If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+...

If `(1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+a_(3)x^(3)+.....+a_(2n)x^(2n)" prove that",a_(0)+a_(2)+a_(4)+.......a_(2n)=(1)/(2)(3^(n)+1)`.

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CHHAYA PUBLICATION|Exercise EXERCISE ( Long answer Type Questions )|40 Videos

  • BINOMIAL THEOREM

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Multiple Correct Answers Type)|5 Videos

  • BINOMIAL THEOREM

    CHHAYA PUBLICATION|Exercise EXERCISE (Very short answer Type Questions )|30 Videos

  • BINOMIAL DISTRUTION

    CHHAYA PUBLICATION|Exercise ASSERTION-REASON TYPE|2 Videos

  • CALCULUS

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2014)|2 Videos

Similar Questions

Explore conceptually related problems

Let (1+x+x^(2))^(9)=a_(0)+a_(1)x+a_(2)x^(2)+.....+a_(18)x^(18) . Then

Let (1+x+x^(2))^(9)=a_(0)+a_(1)x+a_(2)x^(2)+......+a_(18)x^(18) . Then

If (1+x+x^2)^n=a_0+a_1x+a_2x^2+.......+a_(2n)x^(2n) , then prove that a_0+a_2+a_4+....+a_(2n)=1/2(3^n+1) .

If (1+x+x^(2))^(25)=a_(0)+a_(1)x+a_(2)x^(2)+...+a_(50).x^(50) , then a_(0)+a_(2)+a_(4)+....+a_(50) is

If (1+2x+x^(2))^(n) = sum_(r=0)^(2n)a_(r)x^(r) , then a_(r) =

If p(x)=a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)+.....+a_(n-1)x+a_(n)," prove that " underset(xrarra)"lim" p(x)=p(a) .

If (18x^2+12x+4)^n = a_0 +a_(1x)+ a_(2x)^2 +......+ a_(2n)x^(2n) , prove that a_r= 2^n3^r ( "^(2n)C_r + "^(n)C_1 "^(2n-2)C_r + "^(n)C_2 "^(2n-4)C_r + ....

If (1+x-2x^(2))^(6) = 1 + a_(1)x+a_(2)x^(2) + "……" + a_(12)x^(12) , then find the value of a_(2) + a_(4) +a_(6)+ "……" + a_(12) .

If (2x-1)^(8)=a_(8)x^(8)+a_(7)x^(7)+a_(6)x^(6)+..........+a_(1)x+a_(0) , then find the value of a_(0)+a_(1)+a_(2)+.........+a_(7)+a_(8) .

If (x^(2)+x+1)/(1-x) = a_(0) + a_(1)x+a_(2)x^(2)+"…." , then sum_(r=1)^(50) a_(r) equal to

CHHAYA PUBLICATION-BINOMIAL THEOREM -EXERCISE ( short answer Type Questions )
  1. If in the expansion of (1+x)^(m)(1-x)^(n) the coefficients of xandx^(...

    Text Solution

    |

  2. Use binomial theorem to show that if nge1 is an integer then , (a) ...

    Text Solution

    |

  3. n(gt1) is a positive integer . Show that 14^(n)-13n-1 is divisible by...

    Text Solution

    |

  4. For every natural number n(gt1) , show that , 4^(n)+15n-1 is divisible...

    Text Solution

    |

  5. If n is a positive integer (gt1) , show that, (4^(2n+2)-15n-16) is a...

    Text Solution

    |

  6. Using binomial theorem find the value : (0.999)^(4) [correct to thr...

    Text Solution

    |

  7. Using binomial theorem find the value : (1.02)^(4) [correct to two ...

    Text Solution

    |

  8. Write down the expansion of (4x-(y)/(4))^(4). By giving suitable valu...

    Text Solution

    |

  9. Prove that , (x^(n))/(n!)+(x^(n-1).a)/((n-1)!1!)+(x^(n-2).a^(2))/((n-2...

    Text Solution

    |

  10. Two successive terms in the expansion of (2+(1)/(2))^9 are equal . ...

    Text Solution

    |

  11. If n be a positive integer and the sums of the odd terms ans even term...

    Text Solution

    |

  12. If n be a positive integer and the sums of the odd terms ans even term...

    Text Solution

    |

  13. Find the value of (1+x)^(n)+^(n)C(1)(1+x)^(n-1).(1-x)+^(n)C(2)(1+x)^...

    Text Solution

    |

  14. If n be positive integer , show that the algebraic sum of the numerica...

    Text Solution

    |

  15. Show that the sum of the coefficients of the odd terms in the expansio...

    Text Solution

    |

  16. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3)+.....+a(2n)x^(2n)" p...

    Text Solution

    |

  17. If a(r) be the coefficient of x^(r) in the expression of (1+bx^(2)+cx^...

    Text Solution

    |

  18. In a binomial expansion if the coefficients of two successive terms ar...

    Text Solution

    |

  19. Coefficient of x^n in the expansion of (a+x)^(2n)

    Text Solution

    |

  20. If the coefficients of three successive terms in the expansion of (1+...

    Text Solution

    |