Word Form of an Expression

Question

What is the word form of the expression? $$\sum \frac{1}{n^s}$$ That is exactly the way the expression appears in a paper which I am trying to read.

It is $$\sum_{n=1}^\infty \frac{1}{n^s}$$

The sum over $n$ of $1$ divided by $n$ to the power $s$, also you should specify over what you sum, over all $n$? Or what do you mean? — Mathematician 42, Apr 24 '16 at 05:56
$n$ is all whole numbers. I posted the expression exactly as I saw it. — Jeffrey Young, Apr 24 '16 at 06:05
Well yeah, but we are missing context, for all we know $n$ is fixed and you sum over $s$. — Mathematician 42, Apr 24 '16 at 06:07
I don't know what you mean by "the word form". You're not asking about Microsoft Word, are you? — Gerry Myerson, Apr 24 '16 at 06:22
I mean, is it read as "sigma of one divided by n to the power of s"? — Jeffrey Young, Apr 24 '16 at 06:27
Ah. I'd read it as "summation from $n$ equals one to infinity of one over $n$ to the $s$." — Gerry Myerson, Apr 24 '16 at 06:28

score 2 · Accepted Answer · edited Apr 24 '16 at 06:48

2

$A=\frac{1}{n}+\frac{1}{n^2}+...+\frac{1}{n^s}$

$nA=1+\frac{1}{n}+\frac{1}{n^2}+...$

$nA-A=1$

$A=\frac{1}{n-1}$

So the sum equals $\frac{1}{n-1}$.

"summation from n equals one to infinity of one over n to the s."

edited Apr 24 '16 at 06:48

Jeffrey Young

answered Apr 24 '16 at 06:14

Where are the words? – Jeffrey Young Apr 24 '16 at 06:19
What words? ... – Apr 24 '16 at 06:21
Now I see...You didn't ask for a solution, you wanted a word form...Sorry I can't help with that. – Apr 24 '16 at 06:24
It is fine. You have to read carefully and pay attention to fine details. This is none other than Euler's product. I'm just tryin' to learn how to read it. – Jeffrey Young Apr 24 '16 at 06:31
I give you an A for effort. The expression which I asked about came straight from here: http://claymath.org/publications/riemanns-1859-manuscript – Jeffrey Young Apr 24 '16 at 06:42
Thats a nice hypothesis....then my answer is completely wrong...I used a fixed $n$ instead of a fixed $s$... – Apr 24 '16 at 06:54
http://mathworld.wolfram.com/EulerProduct.html https://en.m.wikipedia.org/wiki/Proof_of_the_Euler_product_formula_for_the_Riemann_zeta_function – Jeffrey Young Apr 24 '16 at 07:37
The sum is not the one you wrote: the sum is not over $s$, it's over $n$; $s$ is constant. – Apr 24 '16 at 14:12
Interesting, how you came up with the same reading, word-for-word, that I had posted in a comment earlier, Jeffrey. – Gerry Myerson Apr 24 '16 at 23:55

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