Example 4.5.2. Consider R with the usual metric d. Then we know an open ball of radius E centered at xis simply the open interval (x– E, æ+ €). Let's discuss the convergence ofi). (1/n : n e N)i). (1 +1/n : n € N)For part i): of Example 4.5.2, determine the point x the sequence converges to (an informal argument will suffice). Then, for e= 0.01,nd N such that d(x, 1 + 1=n) < efor all n> N.

Name: Example 4.5.2. Consider R with the usual metric d. Then we know an op
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Description: Example 4.5.2. Consider R with the usual metric d. Then we know an open ball of radius E centered at xis simply the open interval (x– E, æ+ €). Let's discuss the convergence ofi). (1/n : n e N)i). (1 +1/n : n € N)For part i): of Example 4.5.2, deter

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Example 4.5.2. Consider IR with the usual metric d. Then we know an open ball of radius E centered at x is simply the open interval (x– E, æ+ €). Let's discuss the convergence of i). (1/n : n € N) i). (1 + 1/n : n € N) For part i): of Example 4.5.2, determine the point x the sequence converges to (an informal argument will suffice). Then, for e=0,01, nd N such that d(x, 1 + 1=n) < e for all n> N.

Example 4.5.2. Consider IR with the usual metric d. Then we know an open ball of radius E centered at x is simply the open interval (x– E, æ+ €). Let's discuss the convergence of i). (1/n : n € N) i). (1 + 1/n : n € N) For part i): of Example 4.5.2, determine the point x the sequence converges to (an informal argument will suffice). Then, for e=0,01, nd N such that d(x, 1 + 1=n) < e for all n> N.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 63RE

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