Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -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

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

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 21:32:08

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

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

Board footer

Powered by FluxBB