Unformatted text preview: Lectures 7 and 8
• Deﬁnition of a sequence, sequence notation, and examples.
√
1
Ex: an = n2 , bn = (−1)n , xn = n.
• Informal and formal deﬁnitions of the sequence (xn ) converging to x.
• Negation of the sequence (xn ) converging to x.
• Prove 1
n2 → 0. • Prove (−1)n does not converge to any real number x.
• Prove that limits are unique, i.e. if xn → x and xn → y , then x = y .
• Prove n2 +2n
n3 −5 → 0. • Suppose that each sn > 1 and sn → s. Prove 1 √ sn → √
s. ...
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 Winter '11
 Wiley
 Differential Equations, Equations

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