If P(n) is the statement “n 2 + n” is even”, and if P(r) is true, then P(r + 1) is true Given. P(n) = n 2 + n is even and P(r) is true. Prove. P(r + 1) is true

Question

Philoid · Accepted Answer

Given P(r) is true that means,

= r² + r is even

Let Assume r² + r = 2k - - - - - - (i)

Now, (r + 1)² + (r + 1)

r² + 1 + 2r + r + 1

= (r² + r) + 2r + 2

= 2k + 2r + 2

= 2(k + r + 1)

= 2μ

Therefore, (r + 1)² + (r + 1) is Even.

Hence, P(r + 1) is true

If P(n) is the statement “n2 + n” is even”, and if P(r) is true, then P(r + 1) is trueGiven. P(n) = n2 + n is even and P(r) is true.Prove. P(r + 1) is true

If P(n) is the statement “n² + n” is even”, and if P(r) is true, then P(r + 1) is true
Given. P(n) = n² + n is even and P(r) is true.

Prove. P(r + 1) is true