Divergence test help
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Divergence test help

[From: ] [author: ] [Date: 12-11-01] [Hit: ]
2nd : [ 2 n + 9 ] -√ { [2 n + 9]² + 89 } = a_n ,( [ 2n + 9] - √....) ( [ 2n +9] + √.......

∑ (2n+9 - sqrt(4n^2+36n+170))
n=1

use the divergence test to determine whether the series is convergent, divergent, or the test fails.

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1st : Divergence Test is ONLY to determine divergence ,

ie. lim {n --->∞ } a_n ╪ 0 means divergence

2nd : [ 2 n + 9 ] -√ { [2 n + 9]² + 89 } = a_n , thus

( [ 2n + 9] - √....) ( [ 2n + 9] + √....) / ( [ 2n + 9 ] + √....) ≡ - 89 / ( [ 2n + 9 ] + √...) ---> 0

thus " test would fail "...better is that the test reveals nothing ; as it DID NOT fail !
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