Home
Class 11
MATHS
If b(n+1)=1/(1-bn)forngeq1a n db1=b3, t ...

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 `2001` b. `-2001` c. `0` d. none of these

Text Solution

Verified by Experts

By the question, `b_2= 1/(1−b_1)` ​
​`b _3 =2/(1-b_2)` ​
Given `b_3=b_1`
​`⟹b_3=b_1=1/(1−b _2)` ...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Solved Examples And Exercises|9 Videos
  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|482 Videos

Similar Questions

Explore conceptually related problems

If a+b=1, then sum_(n=0)^(n)C(n,r)a^(r)b^(n-r) is equal to '

If m ,n in Na n dm^2-n^2=13 ,t h e n(m+1)(n+1) is equal to a. 42 b. 56 c. 50 d. none of these

If a_(n+1)=(1)/(1-a_(n)) for n>=1 and a_(3)=a_(1) then find the value of (a_(2001))^(2001)

The value of sum_(r=0)^(n)C_(r)/(^(n)C_(r)+^(n)C_(r+1)) equals a.n+1 b.n/2 c.n+2 d.none of these

If (1+t a n1^0)dot(1+t a n2^0)dot(1+t a n3^0)(1+tan45^0)=2^n , then ' n ' is equal to 16 b. 23 c. 3 0 d. none of these

If sintheta=-1/2a n d t a ntheta=1/(sqrt(3))t h e n theta s equal to- 30^0 b.150^0 c.210^0 d.none of these

If omega is a complex nth root of unity,then sum_(r=1)^(n)(a+b)omega^(r-1) is equal to (n(n+1)a)/(2) b.(nb)/(1+n) c.(na)/(omega-1) d.none of these

The value of sum_(r=1)^(n+1)(sum_(k=1)^(k)C_(r-1))( where r,k,n in N) is equal to a.2^(n+1)-2b2^(n+1)-1c.2^(n+1)d. none of these

The value of (lim)_(n rarr oo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!) is a.1b*-1 c.0d .none of these

CENGAGE-SEQUENCES AND SERIES-Solved Examples And Exercises
  1. Each question has four choices a,b,c and d out of which only one is...

    Text Solution

    |

  2. If (1^2-t1)+(2^2-t2)++(n^2-tn)+=(n(n^2-1))/3 , then tn is equal to n^2...

    Text Solution

    |

  3. If b(n+1)=1/(1-bn)forngeq1a n db1=b3, t h e nsum(r=1)^(2001)b r^ 2001 ...

    Text Solution

    |

  4. Let a1, a2, a3, ,a(100) be an arithmetic progression with a1=3a n dsp...

    Text Solution

    |

  5. If 1^2+2^2+3^2++2003^2=(2003)(4007)(334)a n d(1)(2003)+(2)(2002)+(3)(2...

    Text Solution

    |

  6. The value of sum(i=1)^nsum(j=1)^isum(k=1)^j1=220 , then the value of ...

    Text Solution

    |

  7. The sum of 0. 2+0004+0. 00006+0. 0000008+... to oo is (200)/(891) b. ...

    Text Solution

    |

  8. If tn=1/4(n+2)(n+3) for n=1, 2 ,3,.... then 1/t1+1/t2+1/t3+....+1/(t(...

    Text Solution

    |

  9. The coefficient of x^(19) in the polynomial (x-1)(x-2)(x-2^2)(x-2^(19)...

    Text Solution

    |

  10. If 1-1/3+1/5-1/7+1/9-1/(11)+=pi/4 , then value of 1/(1xx3)+1/(5xx7)+1/...

    Text Solution

    |

  11. The positive integer n for which 2xx2^2+3xx2^3+4xx2^4+......+nxx2^n=2...

    Text Solution

    |

  12. If tn denotes the nth term of the series 2+3+6+11+18+...t h e nt(50) ...

    Text Solution

    |

  13. The number of positive integral ordered pairs of (a ,b) such that 6,a ...

    Text Solution

    |

  14. Let a ,b >0, let 5a-b ,2a+b ,a+2b be in A.P. and (b+1)^2, a b+1,(a-1)^...

    Text Solution

    |

  15. The difference between the sum of the first k terms of the serie...

    Text Solution

    |

  16. The value of the sum(n=0)^oo(2n+3)/(3^n) is equal to.

    Text Solution

    |

  17. If the roots of 10 x^3-n x^2-54 x-27=0 are in harmonic oprogresi...

    Text Solution

    |

  18. The 5th and 8th terms of a geometric sequence of real numbers are 7! ...

    Text Solution

    |

  19. Let a ,b ,c ,d be four distinct real numbers in A.P. Then half of the...

    Text Solution

    |

  20. Let a1, a2, a3, ,a(101) are in G.P. with a(101)=25a n dsum(i=1)^(201)...

    Text Solution

    |