@@ -100,7 +100,7 @@ know anything about algebra. One way to see this is to use Inf to compare \verb@ \oo{true} \ii : d<0.01 \oo{true} - \ii : d<10^-10 + \ii : d<0.0000001 \oo{true} \ii : d<0 \oo{false} ch02/ch02.tex @@ -437,5 +437,14 @@ some initial terms. (b) Similarly, prove that convergence is unaffected by multiplying all the terms by some constant factor. \end{hw} +\begin{hw}[2] +Prove the identity +\begin{equation*} + \int_0^1 x^{-x} \der x = \sum_{n=1}^\infty n^{-n} \qquad . +\end{equation*} +This is known as the ``Sophomore's dream,'' because at first glance it looks like the +kind of plausible but false statement that someone would naively dream up.\index{Sophomore's dream} +\end{hw} + \end{hwsection} ch06/ch06.tex 9413dc273ec4aa166bb564d7eafc628af7e35310 Ben Crowell githubcrowell09@lightandmatter.com http://github.com/bcrowell/calculus/commit/66c83406259b2cc1d19ae875e121d75dcbe5ae24 66c83406259b2cc1d19ae875e121d75dcbe5ae24 2009-06-11T09:44:00-07:00 2009-06-11T09:44:00-07:00 Sophomore's dream hw 44891dcb089b93a40e47703f7fcb65ec01da03e5 Ben Crowell githubcrowell09@lightandmatter.com