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SW [0&8 $9.7) Ami-57L vi .151 great: 63. Prove: If the interval of convergence of the series
21°20 ck(x — 2:9)" is (3:0 — R. x0 + R], then the series Enn—
verges conditionally at x0 + R. 00 O0 00
63. The assumption is that Z ckRk is convergent and Z Ck(—R)k is divergent. Suppose that Z ckR"
' Ic=o k=ﬂ k=0 00
is absoluteiy convergent then Zea—Ry“ is also absolutely convergent and hence convergent
because IckRki = [ck(—R)"E, which contradicts the assumption that Zea—R)" is divergent so
chRk must be conditionally convergent.
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- Fall '11