Home
Class 12
MATHS
Let P(n):2^n<(1xx2xx3xxxxn) . Then the s...

Let `P(n):2^n<(1xx2xx3xxxxn)` . Then the smallest positive integer for which `P` `(n)` is true is `1` b. `2` c. `3` d. `4`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    DISHA PUBLICATION|Exercise Exercise-2 Concept Applicator|20 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    DISHA PUBLICATION|Exercise Exercise-2 Concept Applicator|20 Videos

  • MATRICES

    DISHA PUBLICATION|Exercise Exercise 2: Concept Applicator|30 Videos

  • PROBABILITY -2

    DISHA PUBLICATION|Exercise EXERCISE - 2 : CONCEPT APPLICATOR|30 Videos

Similar Questions

Explore conceptually related problems

Let P(n):3^(n) =lambda then smallest value of lambda is

Let P(n) :n^(2)+n is even.Is P(1) is true?

Let P(n): n^(2)-n+41 is a prime number, then

Let P(n) :n^(2) >9 . Is P(2) true?

Let P(n): n^(2)+n is odd, then P(n) Rightarrow P(n+1) for all n. and P(1) is not true. From here, we can conclude that

Let P(n):n^(2)+n+1 is an even integer.If P(k) is assumed true rArr P(k+1) is true. Therefore P(n) is true:

DISHA PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-Exercise-1 Concept Builder
  1. For a positive integer n , let a(n) = 1+ 1/2 + 1/3 +…+ 1/(2^(n)-1) ...

    Text Solution

    |

  2. The statement P(n) 1 x 1! + 2 x 2! + 3 x 3! + …+ n x n! = (n+1)! -1 is...

    Text Solution

    |

  3. Let P(n):2^n<(1xx2xx3xxxxn) . Then the smallest positive integer for w...

    Text Solution

    |

  4. Let P(n):n^2+n+1 is an even integer. If P(k) is assumed true=>P(k+1) i...

    Text Solution

    |

  5. Principle of mathematical induction is used

    Text Solution

    |

  6. For each n in N, the correct statement is

    Text Solution

    |

  7. If n is a natural number then ((n+1)/2)^n ge n! is true when

    Text Solution

    |

  8. For natural number n , 2^n (n-1)!lt n^n , if

    Text Solution

    |

  9. If P(n):2nltn!,ninN then P(n) is true for all le . . . . . . . . . .

    Text Solution

    |

  10. If 4^n/(n+1) lt ((2n)!)/((n!)^2), then P(n) is true for

    Text Solution

    |

  11. For every positive integral value of n, 3 ^(n) gt n^(3) when

    Text Solution

    |

  12. If x gt -1 , then the statement (1+x)^n gt 1 +nx is true for

    Text Solution

    |

  13. For all positive integral values of n, 3^(2n)-2n+1 is divisible by

    Text Solution

    |

  14. For every natural number n, n(n^2-1) is divisible by

    Text Solution

    |

  15. Prove the following by the principle of mathematical induction:\ 2....

    Text Solution

    |

  16. The remainder when 5^(4n) is divided by 13, is

    Text Solution

    |

  17. 10^n+3(4^(n+2))+5 is divisible by (n in N)

    Text Solution

    |

  18. If P(n) is the statement n^3+n is divisible 3 is the statement P(3) tr...

    Text Solution

    |

  19. For all n in N, 3.5^(2n+1)+ 2^(3n+1) is divisble by-

    Text Solution

    |

  20. Prove the following by using the principle of mathematical induction ...

    Text Solution

    |