## Stimulating Sum

**Problem: **Compute

**Solution:** Note that

But, a little manipulation shows this is equal to

Thus,

Which upon remembering some of the definitions is equal to

Where is the Beta function defined by

So,

Now, ignoring issues of uniform convergence (it is justifiable)

But, with a little bit of elbow grease in the partial fractions department this is equal to

Thus,

More generally, it can be shown using exactly the same method that if

That

Which when has the very nice solution

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