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# Tag Archives: Series

## Convergence of a series

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.

## Factorial series

Evaluate the series

**Solution**

## Otto Dunkel Memomorial

Prove that

**Solution**

We have successively:

since for it holds that

## A squared trigamma series

Prove that

**Solution**

Since we have successively:

## Pierre Mounir series

Let . Prove that