From Wikipedia, the free encyclopedia
This is
the user sandbox of Misha622 . A user sandbox is a subpage of the user's
user page . It serves as a testing spot and page development space for the user and is
not an encyclopedia article .
Create or edit your own sandbox here . Other sandboxes: Main sandbox | Template sandbox
Submit your draft for review!
lim
m
→
∞
∑
n
=
1
m
φ
(
z
n
)
m
2
=
3
z
2
ψ
(
z
)
π
2
{\displaystyle \lim _{m\to \infty }\sum _{n=1}^{m}{\frac {\varphi (zn)}{m^{2}}}={\frac {3z^{2}}{\psi (z)\pi ^{2}}}}
∀
z
∈
N
{\displaystyle \forall z\in \mathbb {N} }
lim
m
→
∞
∑
n
=
1
m
σ
k
(
z
n
)
m
k
+
1
=
ζ
(
k
+
1
)
k
+
1
∏
i
=
1
j
p
i
k
e
i
+
1
+
(
p
i
−
1
)
(
1
−
p
i
k
e
i
1
−
p
i
k
)
p
i
∀
z
,
k
∈
N
,
z
=
∏
i
=
1
j
p
i
e
i
{\displaystyle \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}}}}
ζ
(
2
x
+
1
)
=
(
1
x
+
1
)
(
∑
i
=
1
∞
H
i
x
2
i
+
∑
j
=
2
x
ζ
(
j
)
ζ
(
2
x
+
1
−
j
)
)
∀
x
∈
N
{\displaystyle \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} }
2
H
2
g
+
O
2
g
→
2
H
2
O
g
{\displaystyle \mathrm {2H} _{2_{g}}+\mathrm {O} _{2_{g}}\rightarrow \mathrm {2H_{2}O} _{_{g}}}
H
C
l
a
q
→
H
a
q
+
+
C
l
a
q
−
{\displaystyle \mathrm {HCl} _{_{aq}}\rightarrow \mathrm {H} _{_{aq}}^{+}+\mathrm {Cl} _{_{aq}}^{-}}
