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Diverge or converge

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PLEASE SHOW ALL WORK, STEP-BY-STEP, WITH ALL CORRECT NOTATION.
My notation is lousy for some reason the attachment won't come through, so I cut and pasted it below.

Determine whether the following Diverge (D), Converge Conditionally (CC), or Converge Absolutely (AC). Give the rationale for each response. Must show all work and brief summary on why it does or doesn't (D), (CC), or (AC).

∞ ______4_______
∑ (n+1)(n+2)
n=1

Use the limit comparison test to show that the following series converges.

∞ 3n^2 + 5n
∑ ____________
2^n(n^2 + 1)
n=1

Solution Summary

This shows how to determine the divergence or convergence of series.

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1.
First, I show that converges.
For any natural number and , we have

Thus, for any , we can find , then ...

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