Dr. Cavalieri made the statement in his MATH 566 class that a mathematical proof does not
need to follow any formatting constrain - the only constrain being sound logics. As a matter of
fact, the students could write their proofs in verses, if they so wished.
Dan Elliot, a student of the class, had the following solution to one of the exercises. Enjoy!
Homework – MATH566
September 15, 2013
Dan Elliot
1. Prove 1+2+3+. . .+ n = ½ (n+1)
First proof – Proof by poetic addition
Let n = k
The sum of i from one to k
How tedious its addition
I wish a formula lay
satisfying its very condition
I’ll even rewrite it for fun
arranging its terms in reverse
summing i from k to one
In this same way, I shall immerse
Adding in i from k to one
to the original i from one to k
grants me k times k plus one
I’m nearly ready to say olé
The half of k times k plus one
is a grand condensed expression
identical to the original sum
I demand a celebration!