Math Is Fun Forum

har12sh

Member

Registered: 2021-12-23

Posts: 1

Inequality

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

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,837

Re: Inequality

Hi har12sh,

Welcome to the forum!

I think this is how the question looks:

Let's wait till someone deciphers!

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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.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,837

Re: Inequality

Hi peterparkar3999,

Welcome to the forum!

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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.