Sophomore's dream

So I came across this interesting named equation in this faboulous book Mathematics Devotion.(in its Appendix). This is the Sophomore's Dream:

Oh you can turn any definite integral into a summation like that? (no, just happens for those cases listed above).

Its proof is gloriously documented in here: http://en.wikipedia.org/wiki/Sophomore%27s_dream

It is kinda unfortunate I actually don't know/recall all of its proofs ingredients... I think I've seen it all. But that proof is way cool.

As the wiki says, oh there is the Freshman's Dream that erroneously says (x + y)ⁿ = xⁿ + yⁿ.... for poor freshmen who don't know the binomial theorem. High school freshman should know about the binomial theorem.

But I am not so sure if there are too many (college) sophomore know all the ingredients for the Sophomore's Dream...

The Mathematics Devotional book is fabulously written with great math quotes (but without the hardcore equations) and great looking "eye-candies" of computer generated pictures of fractals and other things.

This is for those who truly enjoys mathematics.

There are too many bullies out there portraying math as nerdy geeky with ugly kids wearing broken glasses taped together. Those who know and enjoy math do not look like that. Hollywood needs to treat science and math with respect. I need to see those math themed movies portraying mathematicians as protagonist.