(1 pt) Each of the following statements is an attempt to show that a given serie

Question

(1 pt) Each of the following statements is an attempt to show that a given series is convergent or divergent not using the Comparison Test (NOT the Limit Comparison Test.) For each statement, ente (or"correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter l.) n+1 1. For alln > 2 C 2. For all n 2 D 3. For all n > 2 rali n > 1, ->-' and the series series -diverges, so by the Comparison Test, the series diverges. In(n) >-, and the series converges, so by the Comparison Test, the series converges. n21-5 ardthe series12 ,2-5 converges, so by the Comparison Test, the series diverges, so by the Comparison Test, the series converges, so by the Comparison Test, the series converges diverges. n In(n)nand the series 2 n In(n) 2-n3 1, and the series converges, so by the Comparison Test, the series converges. 3 Note: To get full credit, all answers must be correct. Having all but one correct is worth 50%. Two or more incorrect answers gives a score of 0%.

Explanation / Answer

1)

C

2)
I

Cuz acc to comparison test, ln(n)/n^2 must have been < 1/n^2
for us to say that ln/n^2 is convergemt

3)
I

1/(n^2 - 5) is actually greater than 1/n^2
So, false
I

4)
I

1/(nlnn) < 2/n is true
But 2/n diverges, this is also true
We cannot say anything here
If for example, we had
1/(nlnn) > 2/n, then we can say that since 1/(nlnn) is larger than a divergent series, so 1/nlnn is also divergent
But since 1/nlnn is lesser, we cannot say it is divergent
So, I

5)

I

This is cuz n/(2-n^3) is not >= 0 for n > 1

6)

C

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