∞
∑ (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.
∑ (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.
-
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 !
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 !