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Suppose Σ XK is conditionally convergent, and define k=1 ak = max {xk, 0} and bk = min {xk, 0} ∞ Notice that xk = a + bk and |xk| = ak - bk. Show that ✗ ak and ☐ bk are both divergent. k-1 K-1

Suppose Σ XK is conditionally convergent, and define k=1 ak = max {xk, 0} and bk = min {xk, 0} ∞ Notice that xk = a + bk and |xk| = ak - bk. Show that ✗ ak and ☐ bk are both divergent. k-1 K-1

Algebra & Trigonometry with Analytic Geometry
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 74E
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Suppose Σ XK is conditionally convergent, and define k=1 ak = max {xk, 0} and bk = min {xk, 0} ∞ Notice that xk = a + bk and |xk| = ak - bk. Show that ✗ ak and ☐ bk are both divergent. k-1 K-1
Transcribed Image Text:Suppose Σ XK is conditionally convergent, and define k=1 ak = max {xk, 0} and bk = min {xk, 0} ∞ Notice that xk = a + bk and |xk| = ak - bk. Show that ✗ ak and ☐ bk are both divergent. k-1 K-1
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