Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
You can also prove that $$\displaystyle\lim_n\sqrt[p_n]{\prod_1^n p_i} = e$$$$\displaystyle\lim_n\left(\prod_1^n p_i\right)^{1/p_n} = e$$
(where $p_i$ is the $i$-th prime number and $e$ is Euler's exponential number)
You can also prove that $$\displaystyle\lim_n\sqrt[p_n]{\prod_1^n p_i} = e$$
You can also prove that $$\displaystyle\lim_n\left(\prod_1^n p_i\right)^{1/p_n} = e$$
You can also prove that $\displaystyle \\ \lim_n \\ \\ \sqrt[p_n]{\prod_1^n p_i} = e$$$\displaystyle\lim_n\sqrt[p_n]{\prod_1^n p_i} = e$$
(where $p_i$ is the $i$-ethth prime number and $e$ is Euler's exponential number)
You can also prove that $\displaystyle \\ \lim_n \\ \\ \sqrt[p_n]{\prod_1^n p_i} = e$
(where $p_i$ is the $i$-eth prime number and $e$ is Euler's exponential number)