Home
Class 11
MATHS
A sequence x1, x2, x3,.... is defined b...

A sequence `x_1, x_2, x_3,....` is defined by letting `x_1=2` and `x_k=x_(k-1)/k` for all natural numbers `k,k>=2` Show that `x_n=2/(n!)` for all `n in N`.

Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUATIONS

    RD SHARMA ENGLISH|Exercise All Questions|163 Videos

  • MATHEMATICAL REASONING

    RD SHARMA ENGLISH|Exercise All Questions|182 Videos

Similar Questions

Explore conceptually related problems

A sequence d_(1),d_(2),d_(3) . . . is defined by letting d_(1)=2 and d_(k)=(d_(k-1))/(k), for all natural numbers, k≥2 . Show that d_(n)=(2)/(n!) , for all n in N .

A sequence x_0, x_1,x_2,x_3, ddot is defined by letting x_0=5 and x_k=4+x_(k-1) for all natural number kdot Show that x_n=5+4n for all ""n in N using mathematical induction..

A sequence a_1,a_2,a_3, ... is defined by letting a_1=3 a n d a_k=7a_(k-1) for natural numbers k ,kgeq2. Show that a_n=3.7_n-1 for all n in N .

A sequence a_(1),a_(2),a_(3), . . . is defined by letting a_(1)=3 and a_(k)=7a_(k-1) , for all natural numbers k≥2 . Show that a_(n)=3*7^(n-1) for natural numbers.

A sequence b_(0),b_(1),b_(2), . . . is defined by letting b_(0)=5 and b_(k)=4+b_(k-1) , for all natural number k. Show that b_(n)=5+4n , for all natural number n using mathematical induction.

A sequence b_(0),b_(1),b_(2), . . . is defined by letting b_(0)=5 and b_(k)=4+b_(k-1) , for all natural number k. Show that b_(n)=5+4n , for all natural number n using mathematical induction.

Let a sequence x_(1),x_(2),x_(3),… of complex numbers be defined by x_(1)=0, x_(n+1)=x_(n)^(2)-i for all n gt 1 , where i^(2)=-1 . Find the distance of x_(2000) from x_(1997) in the complex plane.

Let x_1 , x_2 , x_3,....., x_k be the divisors of positive integer n (including 1 and n). If x_1 + x_2 + x_3 + ...... + x_k = 75 Then sum_(i=1)^k (1/x_i) is equal to (A) 75/k (B) 75/n (C) 1/n (D) 1/75

If each of the observations x_(1),x_(2)….x_(n) is in - creased by k. where k positive or negative number, then show that the variance remains unchanged.

Let n and k be positive such that n leq (k(k+1))/2 .The number of solutions (x_1, x_2,.....x_k), x_1 leq 1, x_2 leq 2, ........,x_k leq k , all integers, satisfying x_1 +x_2+.....+x_k = n , is .......

RD SHARMA ENGLISH-MATHEMATICAL INDUCTION-All Questions
  1. Prove by induction that the sum of the cubes of three consecutive n...

    Text Solution

    |

  2. A sequence a1,a2,a3, ... is defined by letting a1=3 a n d ak=7a(k-...

    Text Solution

    |

  3. A sequence x1, x2, x3,.... is defined by letting x1=2 and xk=x(k-1)...

    Text Solution

    |

  4. Show by the Principle of Mathematical induction that the sum Sn, of th...

    Text Solution

    |

  5. Prove that the number of subsets of a set containing n distinct elemen...

    Text Solution

    |

  6. Using the principle of mathematical induction prove that : 1. 3+2. ...

    Text Solution

    |

  7. Prove by the principle of mathematical induction that for all n in N ...

    Text Solution

    |

  8. Using the principle of mathematical induction prove that 1+1/(1+2)...

    Text Solution

    |

  9. Prove by induction that the sum Sn=n^3+3n^2+5n+3 is divisible by 3 for...

    Text Solution

    |

  10. Using the principle of mathematical induction prove that 1/(1. 2. ...

    Text Solution

    |

  11. Using the principle of mathematical induction. Prove that (x^(n)-y^(n...

    Text Solution

    |

  12. Using the principle of mathematical induction prove that 41^n-14^n ...

    Text Solution

    |

  13. Using the principle of mathematical induction, prove that (2^(3n)-1) i...

    Text Solution

    |

  14. Using principle of mathematical induction prove that sqrtn<1/sqrt1+1/s...

    Text Solution

    |

  15. Prove that: 1+2+3+....+ n<((2n+1)^2)/8 for all ""n in Ndot

    Text Solution

    |

  16. Prove that: 1^2+2^2+3^2.....+n^2>(n^3)/3,n in N

    Text Solution

    |

  17. A sequence x0, x1,x2,x3, ddot is defined by lettingx0=5 and xk=4+x(k-1...

    Text Solution

    |

  18. Prove by the principle of mathematical induction that n<2^n"for all"n ...

    Text Solution

    |

  19. Prove by the principle of mathematical induction that for all n in N ...

    Text Solution

    |

  20. Using the principle of mathematical induction, prove that : 1. 2. 3+2...

    Text Solution

    |