Home
Class 11
MATHS
If a(n+1)=1/(1-an) for n>=1 and a3=a1...

If `a_(n+1)=1/(1-a_n)` for `n>=1` and `a_3=a_1`. then find the value of `(a_2001)^2001`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

Let {a_n}(ngeq1) be a sequence such that a_1=1,a n d3a_(n+1)-3a_n=1 for all ngeq1. Then find the value of a_(2002.)

Let {a_n}(ngeq1) be a sequence such that a_1=1,a n d3a_(n+1)-3a_n=1fora l lngeq1. Then find the value of a_(2002.)

Consider the sequence defined by a_n=a n^2+b n+cdot If a_1=1,a_2=5,a n da_3=11 , then find the value of a_(10)dot

If a_1=1a n da_(n+1)=(4+3a_n)/(3+2a_n),ngeq1,a n dif("lim")_(nvecoo)a_n=a , then find the value of adot

If a_n = (a_(n-1) xx a_(n-2))/(2), a_5 = -6 and a_6 = -18 , what is the value of a_3 ?

Let a_1,a_2,.........a_n be real numbers such that sqrt(a_1)+sqrt(a_2-1)+sqrt(a_3-2)++sqrt(a_n-(n-1))=1/2(a_1+a_2+.......+a_n)-(n(n-3)/4 then find the value of sum_(i=1)^100 a_i

Let a_1,a_2,.........a_n be real numbers such that sqrt(a_1)+sqrt(a_2-1)+sqrt(a_3-2)++sqrt(a_n-(n-1))=1/2(a_1+a_2+.......+a_n)-(n(n-3)/4 then find the value of sum_(i=1)^100 a_i

If a_i > 0 for i=1,2,…., n and a_1 a_2 … a_(n=1) , then minimum value of (1+a_1) (1+a_2) ….. (1+a_n) is :

If b_(n+1)=1/(1-b_n)forngeq1a n db_1=b_3, t h e nsum_(r=1)^(2001)b r^ 2001 is equal to a. 2001 b. -2001 c. 0 d. none of these

A sequence of number a_1, a_2, a_3,…..,a_n is generated by the rule a_(n+1) = 2a_(n) . If a_(7) - a_(6) = 96 , then what is the value of a_(7) ?

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. Write the first five terms of the following sequence and obtain the ...

    Text Solution

    |

  2. Prove that the sum to n terms of the series 11+103+1005+ i s(10/9)(10^...

    Text Solution

    |

  3. If a(n+1)=1/(1-an) for n>=1 and a3=a1. then find the value of (a200...

    Text Solution

    |

  4. Determine the number of terms in a G.P., if a1=3,an=96 ,a n dSn=189.

    Text Solution

    |

  5. Let {an}(ngeq1) be a sequence such that a1=1,a n d3a(n+1)-3an=1 for a...

    Text Solution

    |

  6. Let S be the sum, P the product, and R the sum of reciprocals of n ter...

    Text Solution

    |

  7. If the pth term of an A.P. is q and the qth term is p , then find its ...

    Text Solution

    |

  8. Find the product of three geometric means between 4 and 1/4.

    Text Solution

    |

  9. if (m+1)th, (n+1)th and (r+1)th term of an AP are in GP.and m, n and r...

    Text Solution

    |

  10. Insert four G.M.’s between 2 and 486.

    Text Solution

    |

  11. Find the sum 1^2+(1^2+2^2)+(1^2+2^2+3^2)+ up to 22nd term.

    Text Solution

    |

  12. If G is the geometric mean of xa n dy then prove that 1/(G^2-x^2)+1/(G...

    Text Solution

    |

  13. If the A.M. of two positive numbers aa n db(a > b) is twice their geom...

    Text Solution

    |

  14. The sum of infinite number of terms in G.P. is 20 and the sum of their...

    Text Solution

    |

  15. Find the sum of the series 1+2(1-x)+3(1-x)(1-2x)+....+n(1-x)(1-2x) ...

    Text Solution

    |

  16. Prove that 6^(1//2)xx6^(1//4)xx6^(1//8)...oo=6.

    Text Solution

    |

  17. Three numbers are in G.P. whose sum is 70. If the extremes be each mul...

    Text Solution

    |

  18. If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n d z=c+c/(r^2)+c/(r^4)+o...

    Text Solution

    |

  19. Find the sum 1+4+13+40+121+dot

    Text Solution

    |

  20. If each term of an infinite G.P. is twice the sum of the terms foll...

    Text Solution

    |