Surprising identities / equations What are some surprising equations/identities that you have seen, which you would not have expected?
This could be complex numbers, trigonometric identities, combinatorial results, algebraic results, etc.
I'd request to avoid 'standard' / well-known results like $ e^{i \pi} + 1 = 0$.
Please write a single identity (or group of identities) in each answer.
I found this list of Funny identities, in which there is some overlap.

Some zeta-identies have been much surprising to me.       
Let's denote the value $\zeta(s)-1$ as $\zeta_1(s)$ then
$$ \small \begin{array} {}
1 \zeta_1(2) &+&1 \zeta_1(3)&+&1 \zeta_1(4)&+&1 \zeta_1(5)&+&  ... &=&1\\
1 \zeta_1(2) &+&2 \zeta_1(3)&+&3 \zeta_1(4)&+&4 \zeta_1(5)&+&  ... &=&\zeta(2)\\
             & &1 \zeta_1(3)&+&3 \zeta_1(4)&+&6 \zeta_1(5)&+&  ... &=&\zeta(3)\\ 
             & &            & &1 \zeta_1(4)&+&4 \zeta_1(5)&+&  ... &=&\zeta(4)\\ 
             & &            & &            & &1 \zeta_1(5)&+&  ... &=&\zeta(5)\\ 
 ...         & & & & & & & &... &= &  ...
\end{array}
$$
There are very similar stunning alternating-series relations:
$$ \small \begin{array} {}
1 \zeta_1(2) &-&1 \zeta_1(3)&+&1 \zeta_1(4)&-&1 \zeta_1(5)&+&  ... &=&1/2\\
             & &2 \zeta_1(3)&-&3 \zeta_1(4)&+&4 \zeta_1(5)&-&  ... &=&1/4\\
             & &            & &3 \zeta_1(4)&-&6 \zeta_1(5)&+&  ... &=&1/8\\ 
             & &            & &            & &4 \zeta_1(5)&-&  ... &=&1/16\\ 
 ...         & & & & & & & &... &= &  ...
\end{array}
$$
