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
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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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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