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(a) Let k N. Prove that if k2 + k + 5 is even, then (k + 1)2 + (k + 1) + 5 is even. (b)

Chapter 4, Problem 12

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QUESTION:

(a) Let k N. Prove that if k2 + k + 5 is even, then (k + 1)2 + (k + 1) + 5 is even. (b) What is the value of k2 + k + 5 when k = 7? (c) What information do (a) and (b) provide?

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QUESTION:

(a) Let k N. Prove that if k2 + k + 5 is even, then (k + 1)2 + (k + 1) + 5 is even. (b) What is the value of k2 + k + 5 when k = 7? (c) What information do (a) and (b) provide?

ANSWER:

Step 1 of 4

(a)

The statement to be proved is “if  is even, then  is even”.

Assume that “ is even”. Then we have to verify that is even.

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