Chapter 3 - CBU
Chapter 3 - CBU
Chapter 3 - CBU
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Example.(12 continued)Since1Xn=1(13)n 21Xn=13.7. INTRODUCTION TO INFINITE SERIES 1531n 2 n + 1 .✓ 1 ◆ ⇣nr = lim2 n+1n 2 ⌘ ✓ ◆11= lim= limn 2 n + 111n 2n + 1 = 1,n 211n + 1 converges by limit comparison since X 1n converges.21Xn=11p 3n + 1.We compare withr = limThus1Xn=1✓p 13n+1p1n◆1Xn=11p n=1Xn=1n=11n1/2, which diverges as a p-series with p apple 1.⇣n 1/2 ⌘ ✓ hni ◆ 1/2= lim= lim=(3n + 1) 1/2 3n + 1apple ⇣ n⌘ 1/2 ⇣ 1lim= = p3n + 1 3⌘1 6= 0. 31p 3n + 1diverges by limit comparison.
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