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oo Xn; (d) Xn --+ a as n --+ 00; (e) the limit of {xn} exists and equals a. When Xn --+ a as n --+ 00, you can think of Xn as a sequence of approximations to a, and E as an upper bound for the ~rror of these approximations. 1 is chosen so that the error is less than E when n ~ N. In general, the smaller E gets, the larger N must be. ) 35 Chapter 2 36 SEQUENCES IN R Notice by definition that Xn converges to a if and only if IXn - al In particular, Xn ---+ 0 if and only if IXnl ---+ 0 as n ---+ 00 .

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