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As-salamu alaykum...........I have a question....

\[1+\dfrac12+\dfrac13+\ldots=?\]

This can be written as $\zeta(1)$ (don't be afraid if you never saw this, search for Zeta Function).
\[1+\dfrac12+\dfrac13+\ldots=\prod_{p\in\mathbb P}\dfrac{p}{p-1}\]
where $\mathbb P$ is the set of primes.
Why does this hold? Think using unique prime factorization.

Thanks,Masum Bhai

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)