# If P(n) is

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

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