Home
Class 12
MATHS
If (1+x-x^2)^n/(1+x^2)=a0+a1x+a2x^2+...+...

If `(1+x-x^2)^n/(1+x^2)=a_0+a_1x+a_2x^2+...+a_(2n)x^(2n)` then find `a_1+a_3+a_5+...+a_(2n-1)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • Binomial Theorem for Positive Integrel Index

    A DAS GUPTA|Exercise Exercise|113 Videos

  • Application of dy/dx

    A DAS GUPTA|Exercise Exercise|45 Videos

  • Circles

    A DAS GUPTA|Exercise EXERCISE|122 Videos

Similar Questions

Explore conceptually related problems

If (1+x-x^2)^n/(1+x^2)=a_0+a_1x+a_2x^2+...+a_(2n)x^(2n) then find a_0+a_1+a_2+...+a_(2n)

If (1+x-x^2)^n/(1+x^2)=a_0+a_1x+a_2x^2+...+a_(2n)x^(2n) then find a_0-a_1+a_2_...+a_(2n)

If (1+2x-x^2)^n/(1+x^2)=a_0+a_1x+a_2x^2+...+a_(2n)x^(2n) then find a_0+a_2+a_4+...+a_(2n)

If (1+x-x^2)^10/(1+x^2)=a_0+a_1x+a_2x^2+...+a_nx^n+… then find a_1+a_3+a_5+…

If (1+x-x^2)^10/(1+x^2)=a_0+a_1x+a_2x^2+...+a_nx^n+… then find a_0+a_1+a_2+… .

If (1+x-x^2)^10/(1+x^2)=a_0+a_1x+a_2x^2+...+a_nx^n+… then find a_0+a_2+a_4+…

If (1+x-x^2)^10/(1+x^2)=a_0+a_1x+a_2x^2+...+a_nx^n+… then find a_0-a_1+a_2_... .

If (1+x)^n=a_0+a_1x+a_2x^2+...+a_nx^n then find : a_1-a_3+a_5-a_7+… .

Given that (1+x+x^2)^n=a_0+a_1x+a_2x^2+.....+a_(2n)x^(2n) find i) a_0 + a_1 +a_2 .. . . .+ a_(2n) ii) a_0 - a_1 + a_2 - a_3 . . . . + a_(2n) iii) (a_0)^2 - (a_1)^2 . . . . .+ (a_(2n))^2

If (1+x)^n=a_0+a_1x+a_2x^2+...+a_nx^n then find : a_0+a_3+a_6+a_9+… .

A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. If (1+x-x^2)^n/(1+x^2)=a0+a1x+a2x^2+...+a(2n)x^(2n) then find a0-a1+a2...

    Text Solution

    |

  2. If (1+2x-x^2)^n/(1+x^2)=a0+a1x+a2x^2+...+a(2n)x^(2n) then find a0+a2+a...

    Text Solution

    |

  3. If (1+x-x^2)^n/(1+x^2)=a0+a1x+a2x^2+...+a(2n)x^(2n) then find a1+a3+a5...

    Text Solution

    |

  4. The sum of the binomial coefficients in the expansion of (x^2+1/x)^n i...

    Text Solution

    |

  5. The exponent of a binomial exceeds that of another by 3. the sum of th...

    Text Solution

    |

  6. Find the coefficient of x^3 in the expansion of 1+(1+x)+(1+x)^2+(1+x)^...

    Text Solution

    |

  7. Find the coefficients of x^(50) in the expression (1+x)^(1000)+2x(1+x)...

    Text Solution

    |

  8. (b) Find the value of sum(r=m)^n .^rCm,n>m

    Text Solution

    |

  9. Evaluate (""^3C3+""^4C3+""^5C3+...+""^nC3)xx(""^nC3+""^nC4+""^nC5+...+...

    Text Solution

    |

  10. The value of ^n C1+^(n+1)C2+^(n+2)C3++^(n+m-1)Cm is equal to ^m+n C(n-...

    Text Solution

    |

  11. Prove that ""^(n+1)C2+2*sum(k=2)^n""^kC2=sum(k=1)^nk^2

    Text Solution

    |

  12. If (1+x)^n=C0+C1x+C2x^2+...+Cnx^n , find the sum of the following seri...

    Text Solution

    |

  13. Prove that ""^nC0+2*""^nC1+3*""^nC2+...+(n+1)""^nCn=(n+2)2^(n-1)

    Text Solution

    |

  14. Prove that ""^nC0+3*""^nC1+5*""^nC2+...+(2n+1)""^nCn=(n+1)2^(n)

    Text Solution

    |

  15. Prove that ""^nC0-2*""^nC1+3*""^nC2-...+(-1)""^n(n+1)""^nCn=0

    Text Solution

    |

  16. If sn=""^nC0+2*""^nC1+3*""^nC2+...+(n+1)*""^nCn then find sum(n=1)^oos...

    Text Solution

    |

  17. Find the sum :1*""^nC0+2*""^nC1+3*""^nC2+4*""^nC3+…, where n is an odd...

    Text Solution

    |

  18. Show that :""^nC0*m-""^nC1*(m-1)+""^nC2*(m-2)-...+(-1)^n*""^nCn*(m-n)=...

    Text Solution

    |

  19. Evaluate sum(r=1)^npr/r*"^nCr where pr denotes the sum of the first r ...

    Text Solution

    |

  20. Prove by binomial expansion that sum(k=1)^nk^2*"^nCk=n(n+1)2^(n-2)

    Text Solution

    |