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Problem 7.1.7. Let b be a nonzero real number with |b| < 1 and let e > 0. (a) Solve the inequality |b|" < e for n (b) Use part (a) to prove limn→0 b2 = 0. We can negate this definition to prove that a particular sequence does not converge Co zero.

Problem 7.1.7. Let b be a nonzero real number with |b| < 1 and let e > 0. (a) Solve the inequality |b|" < e for n (b) Use part (a) to prove limn→0 b2 = 0. We can negate this definition to prove that a particular sequence does not converge Co zero.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help me solve problem 7.1.7

11:08 A personal.psu.edu/ecb5/ASO Problem 7.1.6. Use the definition of convergence to zero to prove n2 + 4n +1 lim : 0. n3 Problem 7.1.7. Let b be a nonzero real number with 6 < 1 and let ɛ > 0. (a) Solve the inequality |b|" < e for n (b) Use part (a) to prove limn→0 br = 0. We can negate this definition to prove that a particular sequence does not converge to zero. Example 7.1.8. Use the definition to prove that the sequence (1+ (-1)") = (2,0,2, 0, 2, ...) n=0 does not converge to zero. Before we provide this proof, let's analyze what it means for a sequence (sn) to not converge to zero. Converging to zero means that any time a distance ɛ > 0 is II
Transcribed Image Text:11:08 A personal.psu.edu/ecb5/ASO Problem 7.1.6. Use the definition of convergence to zero to prove n2 + 4n +1 lim : 0. n3 Problem 7.1.7. Let b be a nonzero real number with 6 < 1 and let ɛ > 0. (a) Solve the inequality |b|" < e for n (b) Use part (a) to prove limn→0 br = 0. We can negate this definition to prove that a particular sequence does not converge to zero. Example 7.1.8. Use the definition to prove that the sequence (1+ (-1)") = (2,0,2, 0, 2, ...) n=0 does not converge to zero. Before we provide this proof, let's analyze what it means for a sequence (sn) to not converge to zero. Converging to zero means that any time a distance ɛ > 0 is II
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