Home
Class 11
MATHS
Let P(n) be the statement : 2^(n)gt3n. I...

Let P(n) be the statement : `2^(n)gt3n`. IF P(m) is true, show that, P(m+1) is true. Do you conclude that, P(n) is true for all `ninNN` ?

Text Solution

Verified by Experts

The correct Answer is:
`:." "P(n)` is not true for all `ninNN`.
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION

    CHHAYA PUBLICATION|Exercise Exercise|57 Videos
  • MATHEMATICAL INDUCTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams|20 Videos
  • HYPERBOLA

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMS|12 Videos
  • STRAIGHT LINE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Assertion-Reason Type)|2 Videos

Similar Questions

Explore conceptually related problems

If ninNN and (2*1+1)+(2*2+1)+(2*3+1)+ . . .+(2*n+1)=n^(2)+2n+5 is true for n=m, then prove that it is also true for n=m+1. Can we conclude that is is true for all ninNN ?

Let P(n) denote the statement that n^2+n is odd. It is seen that P(n) implies P(n+1) , P(n) is true for all

Let T_(r) be the rth term of an A.P. If m. T_(m) = n.T_(n) , the show that, T_(m+n) = 0 .

Consider the statement : " P(n) : n^(2)-n+41 is prime." Then, which one of the following is true?

The value of n for which n!gt2^(n) will true, are -

The nth term of an A.P. is p, show that, the sum of its first (2n-1) terms is (2n-1)p.

Show that n(P(P(P( phi))))=4

Statement 1: The probability of drawing either an ace or a king from a pack of card in a single draw is 2/13. Statement 2: for two events Aa n dB which are not mutually exclusive, P(AuuB)=P(A)+P(B)-P(AnnB)dot a) statement 1 and 2 both are true and statement 2 is correct explaination for statement 1. (b) statement 1 and 2 both are true but statement 2 is not the correct explaination for statement 1. (c) only statement 1 is true. (d) both the statements are false.

If Aa n dB are two events such that P(A)=1/2a n dP(B)=2/3 . Then show that P(A U B) ge 2/3 .

If P(n)=2+4+6+…..+2n ninN then P(k) =k(k+1) implies P(k+1)=(k+1)(k+2) for all kinN . So we can conclude that P(n)=n(n+1) for:

CHHAYA PUBLICATION-MATHEMATICAL INDUCTION -Sample Questions for Competitive Exams
  1. Let P(n) be the statement : 2^(n)gt3n. IF P(m) is true, show that, P(m...

    Text Solution

    |

  2. If for all ninNN and nge1, then (3^(2^(n))-1) is always divisible by

    Text Solution

    |

  3. If ninNN , both expression n(n+1)(n+2) and n(n+1)(n+5) are multiple of...

    Text Solution

    |

  4. The value of n for which n!gt2^(n) will true, are -

    Text Solution

    |

  5. If n is even then the expression n(n^(2)+20) is divisible by the numbe...

    Text Solution

    |

  6. If p inNN then the expression p^(n+1)+(p+1)^(2n-1) is divisible by the...

    Text Solution

    |

  7. 10^(n)+3*4^(2)+5 is always divisible by the number -

    Text Solution

    |

  8. 3^(2n) when divided by 8 leves the remainder-

    Text Solution

    |

  9. If n be a positive integer, then the digit in the unit's place of 3^(2...

    Text Solution

    |

  10. For a positive integer n,n(n+1)(2n+1) when divided by 6 leaves the rem...

    Text Solution

    |

  11. ninNN,(n+1)^(3)+(n+2)^(3)+(n+3)^(3) when divided by 9, then the remain...

    Text Solution

    |

  12. Match the entries given in left column with those given in right colum...

    Text Solution

    |

  13. Match the entries given in left column with those given in right colum...

    Text Solution

    |

  14. P(n):11^(n+2)+1^(2n+1) where n is a positive integer p(n) is divisib...

    Text Solution

    |

  15. P(n):11^(n+2)+1^(2n+1) where n is a positive integer If P(n) = 14642...

    Text Solution

    |

  16. P(n):11^(n+2)+1^(2n+1) where n is a positive integer If n=3, then th...

    Text Solution

    |

  17. If n be a positive integer and P(n):4^(5n)-5^(4n) P(n) is divisible ...

    Text Solution

    |

  18. If n be a positive integer and P(n):4^(5n)-5^(4n) If P(n) be negativ...

    Text Solution

    |

  19. If n be a positive integer and P(n):4^(5n)-5^(4n) When n=3 then the ...

    Text Solution

    |

  20. underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)...

    Text Solution

    |

  21. Statement - I : For every natural number ((n+4)!)/((n+1)!) is divisibl...

    Text Solution

    |