Home
Class 11
MATHS
A student was asked to prove a statement...

A student was asked to prove a statement P(n) by induction. He proved that `P(k+1)` is true whenever P(k) is true for all `k ge 5 in N` and also that P(5) is true. On the basis of this he conclude that P(n) is true
(i) `AA n in W`
(ii) `AA n gt 5`
(iii) `AA n ge 5`
(iv) `AA n lt 5`

A

`AA n in W`

B

`AA n gt 5`

C

`AA n ge 5`

D

`AA n lt 5`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    ICSE|Exercise MULTIPLE CHOICE QUESTIONS |11 Videos

  • POINTS AND THEIR COORDINATES

    ICSE|Exercise CHEPTER TEST |7 Videos

  • PROBABILITY

    ICSE|Exercise CHAPTER TEST |6 Videos

Similar Questions

Explore conceptually related problems

A student was asked to prove a statement P(n) by using the principle of mathematical induction. He proved that P(n) Rightarrow P(n+1) for all n in N and also that P(4) is true: On the basis of the above he can conclude that P(n) is true.

A student was asked to prove a statement by induction. He proved (i) P(5) is true and (ii) truth of P(n) => truth of P(n+1), n in N . On the basis of this, he could conclude that P(n) is true

Let P(n) be the statement ''(3)^(n)gt n'' . If P(n) is true , prove that P(n + 1) is true.

If P(n) is the statement 2^ngeq3n , and if P(r) is true, prove that P(r+1) is 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^3+n is divisible by 3, prove that P(3) is true but P(4) is not true.

Let P(n) be a statement such that P(n) Rightarrow P(n+1) for all n in NN . Also P(k) is true, k in NN . Then we can conclude that:

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

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

Let P(n) be a statement and let P(n) Rightarrow P(n+1) for all natural number n, then P(n) is true.