Evaluate the product

**Solution**

We are making use of the identity

Hence,

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# Tag: Real Analysis

## A finite product

## A convergent sequence

## A limit

## An eta Dedekind type product

## An integral inequality

A site of university mathematics

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,

If is continuous and its derivative is strictly decreasing in then prove that

if it is also known that and .

**Solution**

Since is strictly decreasing then . Thus, is strictly increasing and . Therefore,

since for all .