Let B = Qn (0, 1) be a subset of R. Consider a function f: N→ B defined by f(n) = an, where an = 1-n n+1' nEN. a) Explain whether f is a bijection. (Note: Both injectivity and surjectivity must be discussed.) ) Prove that the sequence {an} is convergent by the Monotone Convergence The- orem. :) Explain whether the series 1 an is convergent. (Note: The name of the test used must be included.)

Let B = Qn (0, 1) be a subset of R. Consider a function f: N→ B defined by f(n) = an, where an = 1-n n+1' nEN. a) Explain whether f is a bijection. (Note: Both injectivity and surjectivity must be discussed.) ) Prove that the sequence {an} is convergent by the Monotone Convergence The- orem. :) Explain whether the series 1 an is convergent. (Note: The name of the test used must be included.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 72E

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