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ch11_p02 - A sequence is an ordered inﬁnite list of real...

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Unformatted text preview: A sequence is an ordered inﬁnite list of real numbers. For example, 1 l 1 l l ,2, 3’ 4, 5, "‘ is a sequence. We write {52:1 for this sequence?” More formally, a sequence is a function f (n) (where n is a positive inte- ger). We know that , 1 11m —— = 0. 11,—)00 n We say the sequence {51—}:1 converges to 0. Questions What exactly does this mean? Informal deﬁnition of a limit A sequence {an}?=1 converges to a limit L if as we go further along the sequence the terms get closer and closer to L. L 01 02 a4 a5 a3 Example 1 lim — = 0. n—mo n 0 W73 71. l Almost formal deﬁnition of a limit £70 (“gnaw The sequence {an} 31.1 converges to L if or 0V0! 4%) AW) 4% :‘s 4.13% maze, if %«L evmfwé/V. ...
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