TheR

It is Bernard Riemann - student of Gauss - who rescued
the Euler identity between an additive and power series to create
what he called the Zeta function.  Trying to appreciate how this what
put together.

The first term looks friendly enough, and gives a multiplicative.
The (s-1) exponent quickly gives finer terms.

So for Zeta(3), one gets 4/3

For Z(4), it is not 5/4:

Seven is the fourth prime.

*     *     *

Stuck on 2.

Oscillates between zero and 1. Next two items are in service of

making sure a zero appears where required...

Bloats the numbers.

A fraction with the value of s.

All in all, informative for extended cases, s as fractions, negative fractions, complex

numbers...

Try with s = .5; n=200; a modest k.