Examine the convergence of a series

**Solution**

From Taylor’s theorem with integral remainder we have that

However it is known that . Hence,

Exponentiating we get

Thus the series converges.

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Examine the convergence of a series

**Solution**

From Taylor’s theorem with integral remainder we have that

However it is known that . Hence,

Exponentiating we get

Thus the series converges.

The exact same proof shows that the series

diverges.