Suppose ∑ an & ∑ bn are series with only positive terms and ∑ bn is known to be convergent. If an>bn for all n, what can you say about ∑ an? Why? *Choose the correct multiple choice and explain why* Suppose a, and b, are series with only positive terms and b, is known to ben=1n= 1n = 1convergent.8,If a, > bn for all n, what can you say about 2 a,? Why?n = 1We cannot say anything about 2a,.n = 1Z a, converges if and only ifan sinn = 12 a, converges by the Direct Comparison Test.inn = 12 a, diverges if and only if an > bn for some n.n = 12a, diverges by the Direct Comparison Test.n = 1

Suppose a, and b, are series with only positive terms and b, is known to be n=1 n= 1 n = 1 convergent. If a, > b, for all n, what can you say about a,? Why? n = 1 We cannot say anything about 2an. n = 1 8. Z a, converges if and only if n = 1 Σ an s 2 a, converges by the Direct Comparison Test. an n = 1 2 a, diverges if and only if an > bn for some n. n = 1 8. 2 a, diverges by the Direct Comparison Test. in n = 1

Suppose a, and b, are series with only positive terms and b, is known to be n=1 n= 1 n = 1 convergent. If a, > b, for all n, what can you say about a,? Why? n = 1 We cannot say anything about 2an. n = 1 8. Z a, converges if and only if n = 1 Σ an s 2 a, converges by the Direct Comparison Test. an n = 1 2 a, diverges if and only if an > bn for some n. n = 1 8. 2 a, diverges by the Direct Comparison Test. in n = 1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

See similar textbooks