Let .

- Prove that is strictly increasing on .
- If , solve the equation

**Solution**

- It is . However, recalling that
we conclude that is strictly increasing.

- We note that
On the other hand, and hence:

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# Tag: Real Analysis

## An equation!

## A finite product

## A convergent sequence

## A limit

## An eta Dedekind type product

A site of university mathematics

Let .

- Prove that is strictly increasing on .
- If , solve the equation

**Solution**

- It is . However, recalling that
we conclude that is strictly increasing.

- We note that
On the other hand, and hence:

Evaluate the product

**Solution**

We are making use of the identity

Hence,

Let be a strictly increasing sequence of positive integers. Prove that the series , where denotes the least common multiple, converges.

**Solution**

We have successively:

Let . We define the sequence . Prove that

Prove that

**Solution**

Let and . Hence,