Home
Class 12
MATHS
Find value of (x+(1)/(x))^(3)+(x^(2)+(1)...

Find value of `(x+(1)/(x))^(3)+(x^(2)+(1)/(x^(2)))^(3)+"........"+(x^(n)+(1)/(x^(n)))^(3)`.

Text Solution

Verified by Experts

`(x+(1)/(x))^(3)+(x^(2)+(1)/(x^(2)))^(3)+"........"+(x^(n)+(1)/(x^(n)))^(3)=sum_(n=1)^(n)(x^(n)+(1)/(x^(n)))^(3)`
`=sum_(n=1)^(n)(x^(3n)+(1)/(x^(3n))+3(x^(n)+(1)/(x^(n))))`
`=sum_(n=1)^(n)x^(3n)+sum_(n=1)^(n)(1)/(x^(3n))+3sum_(n=1)^(n)x^(n)+3sum_(n=1)^(n)(1)/(x^(n))`
`=(x^(3)(1-x^(3n)))/((1-x^(3)))+((1-x^(3n)))/(x^(3n)(1-x^(3)))+(3x(1-x^(n)))/((1-x))+(3(1-x^(n)))/(x^(n)(1-x))`.
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|7 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

(1)(a+b)+(a^(2)+2b)+(a^(3)+3b)+.... upto n terms =(2)(x+(1)/(x))^(2)+(x^(2)+(1)/(x^(2)))^(2)+(x^(3)+(1)/(x^(3)))^(2)+...(x^(n)+(1)/(x^(n)))^(2)=

Find the sum to n terms of the following series: (x+(1)/(x))^(2)+(x^(2)+(1)/(x^(2)))^(2)+(x^(3)+(1)/(x^(3)))^(2)+(x^(4)+(1)/(x^(4)))^(2)+

The value of lim_(x rarr oo)(2x^((1)/(2))+3x^((1)/(3))+4x^((1)/(4))+......+nx^((1)/(n)))/((2x-3)^((1)/(2))+(2x-3)^((1)/(3))+......+(2x-3)^((1)/(n))) is equal to

The value of lim_(x rarr oo)((2^(x^(n)))^((1)/(e^(x)))-(3^(x^(n)))^((1)/(e^(x))))/(x^(n))

Let f(x)=x+(1-x)x^(3)+(1-x)(1-x^(2))x^(3)+.........+(1-x)(1-x^(2))......*(1-x^(n-1))x^(n);(n>=4) then :

Find the value of (1+x)^(n)+nc_(1)(1+x)^(n-1)*(1-x)+^(n)C_(2)(1+x)^(n-2)(1-x)^(2)+.........+(1-x)^(n)

If x=3, find the value of (x^((1)/(3))+x^(-(1)/(3)))(x^((2)/(3))+x^(-(2)/(3))-1)

Find the sum of the series nC_(0)x^(3n)+(nC_(1))/(2)x^(3(n-1))(3-x^(3))+(nC_(2))/(3)x^(3(n-2))(3-x^(3))^(2)+......+(nC_(n))/(n+1)(3-x^(3))^(n)

The coefficient of x^(n) in (1-(x)/(1!)+(x^(2))/(2!)-(x^(3))/(3!)+...+((-1)^(n)x^(n))/(n!))^(2) is equal to

ARIHANT MATHS-SEQUENCES AND SERIES-Exercise (Subjective Type Questions)
  1. If the first four terms of an arithmetic sequence are a,2a,b and (a-6-...

    Text Solution

    |

  2. If 1/1^2+1/2^2+1/3^2+...oo=pi^2/6 then value of 1-1/2^2+1/3^2-1/4^2+.....

    Text Solution

    |

  3. If the arithmetic mean of a(1),a(2),a(3),"........"a(n) is a and b(1),...

    Text Solution

    |

  4. If a(1),a(2),a(3),"........" is an arithmetic progression with common ...

    Text Solution

    |

  5. If t(1)=1,t(r )-t( r-1)=2^(r-1),r ge 2, find sum(r=1)^(n)t(r ).

    Text Solution

    |

  6. Prove that I(1),I(2),I(3)"..." form an AP, if (i) I(n)=int(0)^(pi)(...

    Text Solution

    |

  7. Consider the sequence S=7+13+21+31+".....+"T(n) , find the value of T(...

    Text Solution

    |

  8. Find value of (x+(1)/(x))^(3)+(x^(2)+(1)/(x^(2)))^(3)+"........"+(x^(n...

    Text Solution

    |

  9. If a(m) be the mth term of an AP, show that a(1)^(2)-a(2)^(2)+a(3)^(2)...

    Text Solution

    |

  10. If three unequel numbers are in HP and their squares are in AP, show ...

    Text Solution

    |

  11. Ifa(1),a(2),a(3),"........",a(n) are in AP with a(1)=0, prove that (a(...

    Text Solution

    |

  12. Balls are arranged in rows to form an equilateral triangle. The first ...

    Text Solution

    |

  13. If theta(1),theta(2),theta(3),".......",theta(n) are in AP whose commo...

    Text Solution

    |

  14. Show that,(1+5^(-1))(1+5^(-2))(1+5^(-4))(1+5^(-8))"....."(1+5^(-2n))=(...

    Text Solution

    |

  15. Evaluate S=sum(n=0)^n(2^n)/((a^(2^n)+1) (where a>1).

    Text Solution

    |

  16. Find the sum to infinite terms of the series tan^(-1)((1)/(3))+tan^(-1...

    Text Solution

    |

  17. Find the sum to n terms, whose nth term is tan[alpha+(n-1)beta]tan (al...

    Text Solution

    |

  18. If sum(r=1)^(n)T(r)=(n)/(8)(n+1)(n+2)(n+3)," find "sum(r=1)^(n)(1)/(T(...

    Text Solution

    |

  19. If s1,s2,s3 denote the sum of n terms of 3 arithmetic series whose fir...

    Text Solution

    |

  20. The friends whose ages from a G.P. divide a certain sum of money in pr...

    Text Solution

    |