jsevenpro998
Answered

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10) Using Limit Comparison Test (LCT), the following series
+00
M:
-1 + 2n5
n6 + 1
n=1​

10 Using Limit Comparison Test LCT The Following Series00M1 2n5n6 1n1 class=

Sagot :

LammettHash

Compare to the divergent series,

[tex]\displaystyle\sum_{n=1}^\infty\frac1n[/tex]

Then by the limit comparison test, the given series also diverges, since the limit

[tex]\displaystyle\lim_{n\to\infty}\frac{\frac{2n^5-1}{n^6+1}}{\frac1n} = \lim_{n\to\infty}\frac{2n^6-n}{n^6+1}=\lim_{n\to\infty}\frac{2-\frac1{n^5}}{1+\frac1{n^6}}=2[/tex]

is positive and finite.

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