User:Misha622/sandbox

$\lim _{m\to \infty }\sum _{n=1}^{m}{\frac {\varphi (zn)}{m^{2}}}={\frac {3z^{2}}{\psi (z)\pi ^{2}}}$ $\forall z\in \mathbb {N}$

$\lim _{m\to \infty }\sum _{n=1}^{m}{\frac {\sigma _{k}(zn)}{m^{k+1}}}={\frac {\zeta (k+1)}{k+1}}\prod _{i=1}^{j}{\frac {p_{i}^{ke_{i}+1}+(p_{i}-1)({\frac {1-p_{i}^{ke_{i}}}{1-p_{i}^{k}}})}{p_{i}}}\forall z,k\in \mathbb {N} ,z=\prod _{i=1}^{j}{p_{i}^{e_{i}}}$

$\zeta (2x+1)=({\frac {1}{x+1}})(\sum _{i=1}^{\infty }{\frac {H_{i}}{x^{2i}}}+\sum _{j=2}^{x}{\zeta (j)\zeta (2x+1-j)})\forall x\in \mathbb {N}$

$\mathrm {2H} _{2_{g}}+\mathrm {O} _{2_{g}}\rightarrow \mathrm {2H_{2}O} _{_{g}}$

$\mathrm {HCl} _{_{aq}}\rightarrow \mathrm {H} _{_{aq}}^{+}+\mathrm {Cl} _{_{aq}}^{-}$

7 3Li

+

n

→

4 2He

+

3 1T

+

n