Home
Class 11
MATHS
Give an example of a statement P(n) such...

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

Text Solution

Verified by Experts

The correct Answer is:
`P(n):3n^(2) +n ` is divisible by 3 and so on
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PRINCIPAL OF MATHEMATICAL INDUCTION

    CBSE COMPLEMENTARY MATERIAL|Exercise Very Short Answer Type Questions(M.C.Q)|3 Videos
  • PRACTICE PAPER-II

    CBSE COMPLEMENTARY MATERIAL|Exercise Section-D (Long Answer Type-I)|7 Videos
  • PROBABILITY

    CBSE COMPLEMENTARY MATERIAL|Exercise LONG ANSWER TYPE QUESTIONS|23 Videos

Similar Questions

Explore conceptually related problems

Given an example of a statement P(n) such that it is true of all nN.

Given an example of a statement P(n) which is true for all n>=4 but P(1),P(2) and P(3) are not true.Justify your answer.

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.

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(n+1)(n+2) is divisible is 12 prove that the statements P(3) and P(4) are true,but that P(5) is not true.

If P(n) is a statement (n in N) such that if P(k) is true,P(k+1) is true for k in N, then P(k) is 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)>=3n. If P(r) is true,show that P(r+1) is true.Do you conclude that P(n) is true for all n in N

If P(n) is the statement n^(2)+n is even,and if P(r) is true then P(r+1) is true.

If P(n) is the statement n^(2)>100, prove that whenever P(r) is true,P(r+1) is also true.