If P (n) is the statement “n3 + n is divisible by 3”, prove that P (3) is true but P (4) is not true.

Question

If P (n) is the statement “n³ + n is divisible by 3”, prove that P (3) is true but P (4) is not true.

Asked by Sakshi | 1 year ago | 118

0 0

Class 11 Maths Principle of Mathematical Induction Add Answer

a + (a + d) + (a + 2d) + … + (a + (n-1)d) = \( \dfrac{n}{2}\) [2a + (n-1)d]

7²ⁿ + 2^{3n – 3}. 3n – 1 is divisible by 25 for all n ϵ N

(ab)ⁿ = aⁿ bⁿ for all n ϵ N

Accepted Answer

Given:

P (n) = n³ + n is divisible by 3

We have P (n) = n³ + n

So,

P (3) = 3³ + 3

= 27 + 3

= 30

P (3) = 30, So it is divisible by 3

Now, let’s check with P (4)

P (4) = 4³ + 4

= 64 + 4

= 68

P (4) = 68, so it is not divisible by 3

Hence, P (3) is true and P (4) is not true.

Answered by Aaryan | 1 year ago