Question

1. Decide if the following statements are true or false. Give an explanation for your answer. (a) If 0 < an < bn and Σ an converges, then Σ bn converges (b) If 0 < an < bn and Σ an diverges, then Σ bn diverges. (c) If bn an 0 andbcoverges, then an converges (d) If Σ an converges, then Σ|an| converges (e) If Σ an converges, then linn lan +1/a (f) Σχ00(-1)"cos(nn) is an alternating series (g) The power series Σ_ has a radius of convergence of (h) If the terms an approach zero as n increases, then the series Σ an converges (i) If Σ an diverges and Σ bn diverges, then Σ(an +bn) diverges (j) Λ power scries always converges at at least onc point. (k)-3 < x < 2 could be the interval of convergence of Σ CnXn. converges, then lim an+an 1 The series Σοοι 2(-1)"

Answer 1

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