Determine whether each of the following sequences converge or not. In each case present a formal explanation. If a sequence converges find the limit and if not determine whether there should be any converging subsequences, and if so find more than one converging subsequences. Xk+1 = (k/k+2)Xk, where X1 = 1/2 Attempt: Now I was thinking of taking the (lim k-->∞ 1/(1+2/k) ) (lim k-->∞ Xk). In other words take the limits of the individual sequences and show that they converge, but I'm realizing I don't have an expression for Xk so I might not be able to do this. In the same breath if this sequence doesn't converge, would finding two subseqeunces through by fiddling with some numbers work?