Assalamu alaykum...........I have a question....
\[1+\dfrac12+\dfrac13+\ldots=?\]
Sequence

 Posts: 2
 Joined: Fri Aug 21, 2015 9:17 pm
Re: Sequence
This can be written as $\zeta(1)$ (don't be afraid if you never saw this, search for Zeta Function).
\[1+\dfrac12+\dfrac13+\ldots=\prod_{p\in\mathbb P}\dfrac{p}{p1}\]
where $\mathbb P$ is the set of primes.
Why does this hold? Think using unique prime factorization.
\[1+\dfrac12+\dfrac13+\ldots=\prod_{p\in\mathbb P}\dfrac{p}{p1}\]
where $\mathbb P$ is the set of primes.
Why does this hold? Think using unique prime factorization.
One one thing is neutral in the universe, that is $0$.
Re: Sequence
It's a divergent series. Neither the infinite sum nor the infinite product has a finite value. So it does not even make sense to say that they are equal. More details: https://en.wikipedia.org/wiki/Harmonic_ ... thematics)
"Everything should be made as simple as possible, but not simpler."  Albert Einstein