Mathematics Homework Solutions
#160989
Proof methods & strategy
Problem: Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive?
This provides an example of a positive integer proof.
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- Show that (2 + √2)^n + (2 - √2)^n is an integer for all positive integers n by using the biomial theorem. - Show that (2 + √2)^n + (2 - √2)^n is an integer for all positive integers n by using the binomial theorem.
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- Induction Proof - see attachment.
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