Home
Class 11
MATHS
Let P(n) denote the statement: 2^(n)ge n...

Let P(n) denote the statement:
`2^(n)ge n!`.Show that P(1),P(2),P(3) are true butP(4) is not true.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION

    MODERN PUBLICATION|Exercise CHECK YOUR UNDERSTANDING|10 Videos

  • MATHEMATICAL INDUCTION

    MODERN PUBLICATION|Exercise CHAPTER TEST 4|12 Videos

  • MATHEMATICAL INDUCTION

    MODERN PUBLICATION|Exercise Exercise|10 Videos

  • LINEAR INEQUATIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • MATHEMATICAL REASONING

    MODERN PUBLICATION|Exercise CHAPTER TEST 14|12 Videos

Similar Questions

Explore conceptually related problems

Let P(n) be the statement : 3^(n)gt n What is P(n+1) ?

Let P(n) be the statement : 2^(n)gt 1 . Is P(1) true ?

Give an example of a statement P(n) such that P(3) is true, but P(4) is not true.

If P(n) is the statement n^(3)+n is divisible by 3, prove that P(3) is true but P(4) is not true.

If P(n) is the statement n^(2)-n+41 is prime. Prove that P(1),P(2) and P(3) are true. Prove also that P(41) is not true.

Let P(n) be the statement 3^(n)>n. If P(n) is true,P(n+1) is also true.

Let P (n) be the statement 2^(n) ge n . When P (r) is true, then is it true that P (r + 1) is also true ?

if P(n) be the statement 10n+3 is a prime number", then prove that P(1) and P(2) are true but P(3) is false.