recitation-3-sol.pdf - Analysis Fall 2017 Recitation 3...

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Analysis Fall 2017 Recitation 3: Sequences 09/29/2017 Exercise 2.1.6 (Warm-up) Is the sequence ( n n 2 +1 ) convergent ? If yes, specify the limit. Use only the definition of a convergent sequence to answer this question.
Exercise 2.2.6 (Warm-up) Let x n = 1 n y n = 1 n 2 z n = x n y n w n = y n x n Do these sequences converge ? What are their limits ? Can we apply the quotient rule for limits ? Why or why not ?
Exercise 2.2.9 Let ( x n ) be a sequence such that for some x R the limit lim n + | x n +1 - x | | x n - x | exists and is < 1 . Show that ( x n ) converges to x. 1
Analysis Fall 2017

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