Question

i want the sum of series:
√2+√2+√2+√2+.........infinity
and there is a big underroot and then inh and in
that i cant draw

Answer 1

\[let y=\sqrt{2+\sqrt{2+\sqrt{2........}}}\] \[y ^{2}=2+\sqrt{2+\sqrt{2+......}}\]\[y ^{2}=2+y\]\[y ^{2}-y-2=0\]gives you y=2,-1.
where -1 is a redundant root came due to the squaring so y=2.