# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2021-12-23 23:39:42

har12sh
Member
Registered: 2021-12-23
Posts: 1

### Inequality

$$\text { 35. Let, } x_{n}=\sqrt[2]{2+\sqrt[3]{3+\sqrt[4]{4+\cdots+\sqrt[n]{n}}}} ; \text { prove that } x_{n+1}-x_{n}<\frac{1}{n !}, n=2,3, \ldots .$$

Offline

## #2 2021-12-24 00:29:54

ganesh
Registered: 2005-06-28
Posts: 35,588

### Re: Inequality

Hi har12sh,

Welcome to the forum!

I think this is how the question looks:

Let's wait till someone deciphers!

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

## #3 2021-12-24 20:29:35

peterparkar3999
Banned
From: USA
Registered: 2021-12-24
Posts: 1
Website

hi

Offline

## #4 2021-12-24 21:32:08

ganesh
Registered: 2005-06-28
Posts: 35,588

### Re: Inequality

Hi peterparkar3999,

Welcome to the forum!

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline