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Solutions to Assignment-2 - University of California, Berkeley
math.berkeley.edu!k!1 xg: (a)Show that L= limsupa n if and only if L= supS. Solution: Suppose L= limsupa n. First, we claim that L2S. ... Since the right hand side is the tail end of a converging series, by the Cauchy criteria, for any ">0, there exists an Nsuch that for any n;m>N, the right hand side can be made smaller than ". This shows that fr