Find $ S_{20} $ if $ \frac{ a_{n} +2}{2} = \sqrt{2S_{n}} $ for all integer n Define $ a_{n} $ is a sequence and all terms of $ a_{n} $ are positive. $ S_{n} $ is the summation of the first n terms. If $ \frac{ a_{n} +2}{2} = \sqrt{2S_{n}} $ for all integer n, then find $ S_{20} $

$$\frac{a_1+2}{2}=\sqrt{2a_1} \Leftrightarrow (\sqrt{a_1}-\sqrt{2})^2=0$$
Thus
$$S_1=a_1=2$$
Next
$$\frac{ S_n-S_{n-1} +2}{2} = \sqrt{2S_n} \Leftrightarrow (\sqrt{S_n}-\sqrt{2})^2=S_{n-1}\Leftrightarrow \sqrt{S_n}=\sqrt{S_{n-1}}+\sqrt{2}$$
Let $T_n=\sqrt{S_n}$.
Then $T_1=\sqrt{2}$ and 
$$T_n =T_{n-1}+\sqrt{2}$$
Can you find $T_{20}$?
