Suppose that xn x and the sequence (yn) is bounded. Show that
lim (xn + yn) = lim xn + lim (yn).
I know that since (xn) converges lim xn = lim (xn) and that
___ __ ___
lim (xn + yn) </= lim xn + lim yn.
Thus the equality in this equation must come from the fact that (yn) is bounded, but I am not sure how to get there. Please help.
Sequences and Limit Superior are investigated.