For any nonnegative integer , define

Evaluate the limit .

**Solution**

**Lemma: **Let and . It holds that

*Proof: *The LHS is just the imaginary part of

This is a geometric progression , hence:

The result follows.

Hence,

Now,

A site of university mathematics

Home » Uncategorized » A limit

For any nonnegative integer , define

Evaluate the limit .

**Solution**

**Lemma: **Let and . It holds that

*Proof: *The LHS is just the imaginary part of

This is a geometric progression , hence:

The result follows.

Hence,

Now,