In lecture 29, we looked at explicit Zeta sums like 1+2+3+ ...+ n or
12+22+32 + .. + n2.
There are explicit formulas for that. More generally, one can look
at 1-s+2-s+3-s + .. + n-s
and especially look at the limit when n going to infinity. This is the zeta
function ζ(s) = 1-s+2-s+3-s + ... .
In the following movie, we look at the roots of this function
by plotting 1/zeta(s). One needs calculus to make sense of expressions like
ζ(-1) = 1+2+3+4+.... . The limit is (it should surprise you) -1/12.
See the Numberphile movie.
The plotting is done in Google earth:
Poll from lecture 29
This is a good poll. It exposes a misconception.
The correct answer is B and was not always chosen by the majority
in both sections. The problem of
An article in MAA.
Poll from lecture 30
Also this poll shows that already just getting the meaning the fundamental theorem
of calculus can be tricky. In this case, the correct answer is B.
