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**Inequality**

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

$$

\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 .

$$

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

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.

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**peterparkar3999****Banned**- From: USA
- Registered: 2021-12-24
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hi

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

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.

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**Inequality**