18.014 Final Comments and Grades
Lemma: You can check that if p(x) is a polynomial with rational coefficients, then
Note that 1+x+x^2 + ... = 1/(1-x); this converges for x=1/2 (or indeed for any x between -1 and 1). Show that if you apply x d/dx to 1/(1-x) 100 times, and plug in x=1/2, you get the desired sum, and (using the lemma) that this is rational.
(That is the kernel of the solution; if you'd like to hear more details, just ask!)
(Congratulations to Russell Moriarty for solving this very hard problem!)
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