Home
Class 11
MATHS
Applying P.M.I. prove that x^n-y^n is a...

Applying P.M.I. prove that `x^n-y^n` is always divisible by x+y where n is a pos. even integer

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    PATHFINDER|Exercise QUESTION BANK|225 Videos

  • CARTESIAN COORDINATES AND STRAIGHT LINE

    PATHFINDER|Exercise QUESTION BANK|249 Videos

Similar Questions

Explore conceptually related problems

Show that 9^(n+1)-8n-9 is divisible by 64, where n is a positive integer.

Prove that x^(n)-y^(n) is divisible by (x-y) for all n""inNN

Applying the principle mathematical induction (P.M.I.) show that 5^(2n+2)-24n-25 is always divisible by 576 where n is a natural number.

For + ve integer n,n^(3)+2n is always divisible by

(1+x)^n-nx-1 is divisible by (where n in N)

By principle of mathematical induction show that a^(n)-b^(n) is divisible by a+b when n is a positive even integer.

By induction method prove that, (a^(n)+b^(n)) is divisible by (a+b) when n is an odd positive integer .

By using mathematical induction prove that 3^(2n)-8n-1 is divisible by 64 when n is an integer.

Applying P.M.I. prove that (1+x)^n gt 1+nx where n is a pos integer and nge2 :xgt(-1)

Using the principle of mathematical induction ,prove that x^n-y^n is divisible by (x-y) for all n in N .

PATHFINDER-BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION-QUESTION BANK
  1. If coefficient of x^2 and x^11 are 27 and -192 respectively of (1+ax+2...

    Text Solution

    |

  2. Find the coefficient of x^5 in the expansion of (1+x)^21+(1+x)^22+...+...

    Text Solution

    |

  3. Determine the x-independent term in the expansion of (1+4x)^p(1+1/(4x)...

    Text Solution

    |

  4. For ninN , 2^(3n)-1 is divisible by

    Text Solution

    |

  5. For ninN , n^3+2n is divisible by

    Text Solution

    |

  6. ForninN , 3^(2n-1)+2^(n+1) is always divisible by

    Text Solution

    |

  7. For ninN 2^(3n)-7n-1 is always divisible by

    Text Solution

    |

  8. The greatest positive integer divides (n+1)(n+2)..........(n+r) is

    Text Solution

    |

  9. Applying the principle of mathematical induction (P.M.I.) prove that 1...

    Text Solution

    |

  10. Using mathematical induction show 7+77+777+......+n terms =7/81(10^(n+...

    Text Solution

    |

  11. Applying P.M.I. prove that x^n-y^n is always divisible by x+y where n...

    Text Solution

    |

  12. Applying the principle mathematical induction (P.M.I.) show that 5^(2n...

    Text Solution

    |

  13. Applying P.M.I. prove that (1+x)^n gt 1+nx where n is a pos integer an...

    Text Solution

    |

  14. Prove that (costheta+isintheta)^n=cosntheta+isinntheta by P.M.I. where...

    Text Solution

    |

  15. For which natural numbers n the inequality 2^ngt2n+1is true?

    Text Solution

    |

  16. For n being a natural number prove that 1.1!+2.2!+3.3!+.....+n.n! =(n+...

    Text Solution

    |

  17. For ninN, prove that ((n+1)/2)^ngt n!

    Text Solution

    |

  18. Show that 101^(50)gt 99^(50)+100^(50)

    Text Solution

    |

  19. Using P.M.I. prove that 2^ngt n for all nge1:ninN

    Text Solution

    |

  20. If nge3 is an integer prove that 2n+1 lt 2^n by P.M.I.

    Text Solution

    |