Question
Asked Mar 9, 2020
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Determine if the following series converges or diverges. Give reasons for your answer.
1+2+3+ ... +n
n=1
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Determine if the following series converges or diverges. Give reasons for your answer. 1+2+3+ ... +n n=1

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Expert Answer

Step 1

Given series is

Calculus homework question answer, step 1, image 1

We know that

Calculus homework question answer, step 1, image 2

Therefore, we have

Calculus homework question answer, step 1, image 3

Step 2

Now we use limit comparision test to check the convergence and divergence of given series, so we consider the following series

Calculus homework question answer, step 2, image 1

Since the limit is non-zero finite, so both series converge and diverge together.

The series Calculus homework question answer, step 2, image 2 converges by p-series test 

Hence given series converges

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