Question
Asked Nov 4, 2019
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Help please

[3]
Use the Limit Comparison Test to determine if the series
Σ.
1
converges or
Inn
n=2
Σ.
diverges. (Hint: compare to
.t
Kt
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[3] Use the Limit Comparison Test to determine if the series Σ. 1 converges or Inn n=2 Σ. diverges. (Hint: compare to .t Kt

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Expert Answer

Step 1

Consider the given series:

1
/Inn
n-2
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1 /Inn n-2

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Step 2

Now, further

Since,

In n
then
In n
1
1
Vinn
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In n then In n 1 1 Vinn

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Step 3

It is known that, the series ∑ is divergent by p-series test, since here p=1/2, which is less than 1, hence divergent.

Now, by limit comparison test: for two series an and bn such that an ≤ bn then if ∑an is divergent then so is ∑bn...

1
/In n
1
is divergent
Vn
and
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1 /In n 1 is divergent Vn and

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