(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have to test this series for convergency/divergency

Ʃ1000(3/4)^n - n/(n+10000)

n=1 to ∞

3. The attempt at a solution

At first I thought of analyzing both parts separately, (3/4)^n is a geometric series with r < 1 and so it converges, and applying the root test to n/(n+10000). Then I'd have the sum of two convergent series that ofc, also converges.

Went to test my hypothesis on WolframAlpha, and it actually told me the series diverges by the limit test, wich I verified to be true.

So my question is, why was the method I used, wrong?

Thanks in advance!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Divergence/Convergency of a series

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