Daniel Morales asked a few great questions from pg 573 of Larson (infinite series).
Most of his questions (#27-28, 33-36) have to do with partial fractions. Here is a quick review if you have forgotten how to do partial fractions. Its very useful for taking a rational expression and ‘breaking’ it into smaller terms that are easier to work with, compute or cancel out. We will use this technique in integration and also for infinite sums.
I have worked out problem #27 in its entirety for your reference, including some notes on using the TI-89 to do sums and on partial fractions. For part c of #27, this graphing calc image may be useful:
Larson, pg 573, #27c
Daniel also asked about problems #45-46. These are actually just infinite geometric series (from Algebra II). You can break the sum into smaller sums to find its value. Here is the solution to #45:
Infinite Geometric Series
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Mr. Bourbois 