Use Mathematical Induction to prove that whenever n is a positive integer 2 divides n2-n.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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Use Mathematical Induction to prove that whenever n is a positive integer 2 divides n-n.
Transcribed Image Text:Use Mathematical Induction to prove that whenever n is a positive integer 2 divides n-n.
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We use Mathematical Induction to prove that whenever n is a positive integer 2 divides n2-n.

The proof consists of three steps:

(i) In this step we check the validity of the statement for n=1.

(ii) In this step we assume the statement is true for n=k, where k is any positive integer.

(iii) In the final step we wish to show that the statement is also true for n=k+1 whenever it is true for n=k.  

For the proof of the statement see the next sections.

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