Simple versus formal proof?

Is there a useful (for any possible meaning of the word "useful") more
formal proof for k^2 + k being even for all k other than simply listing
the two cases for k being odd and even and referring to the sums of two
odd or two even numbers being even? E.g. it's easy to prove it by
induction:

1^2 + 1 = 2

(k+1)^2 + (k+1)
= k^2 + 3k + 2
= (k^2 + k) + 2k + 2

Are there ever any reasons for wanting a more "formal" looking proof?

Cheers,

Ross-c

.

Relevant Pages

  • Re: Simple versus formal proof?
    ... Is there a useful (for any possible meaning of the word "useful") more ... formal proof for k^2 + k being even for all k other than simply listing ... the two cases for k being odd and even and referring to the sums of two ... induction you've got to do the other direction, ...
    (sci.math)
  • Re: Simple versus formal proof?
    ... formal proof for k^2 + k being even for all k other than simply listing ... the two cases for k being odd and even and referring to the sums of two ... induction doesn't do it. ...
    (sci.math)
  • Re: Simple versus formal proof?
    ... formal proof for k^2 + k being even for all k other than simply listing ... the two cases for k being odd and even and referring to the sums of two ... Yes, to show other methods, easier than induction. ... k^2 is even and k^2 + k is sum of two even numbers, ...
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  • Re: gcd(n,n +1) = 1
    ... Sara wrote, ... i search in many web sites about this: ... it is odd. ... a formal proof. ...
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  • Re: Help. What is a model?
    ... Stop insisting that content recapitulates meaning. ... "Understanding Godel isn't about following his formal proof. ... That would make a mockery of everything Godel was up to." ...
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