Question

alternating series

Answer 1

converges for sure
series alternates, it is enough to check that the terms to go zero as n goes to infinity, which they do

Answer 2

http://jtaylor1142001.net/calcjat/Solutions/Series/Alternating-Series/Alternating-Series-1/Alternating-Series-1-Layers.htm

nice article here

Answer 3

says that it converges