If P(n) is the statement “n2 + n” is even”, and if P(r) is true, – InterviewSolution

InterviewSolution

1.

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

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

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