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**MisterMaths****Member**- Registered: 2017-05-13
- Posts: 2

This is about sequences and series, to be more precise it is about finding their nature which is either divergent or convergent by using different methods (Cauchy, D'Alembert, Reiman...). I study maths in french so somethings might not make sense since they are directly translated by me but after all maths is one language.

I was to determine whether this sequence is convergent or divergent: Un=

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 692

I think it is divergent.

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**greg1313****Member**- Registered: 2016-12-19
- Posts: 14

MisterMaths wrote:

I was to determine whether this sequence is convergent or divergent: Un=http://i.imgur.com/BOwr53L.png

That sequence is convergent.

As n approaches infinity, each expression on either side of the subtraction sign approaches 1. That answers the part of convergence/the question.

(If you were being asked about what value the whole expression is approaching, then you would know the value of the expression on the left-hand

side of the subtraction sign is greater for all (finite) values of n than the right-hand expression. So, the value of the whole sequence would be a

finite number greater than or equal to 0, but less than 1. I would expect the value to equal to 0.)

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**MisterMaths****Member**- Registered: 2017-05-13
- Posts: 2

greg1313 wrote:

MisterMaths wrote:I was to determine whether this sequence is convergent or divergent: Un=http://i.imgur.com/BOwr53L.png

That sequence is convergent.

As n approaches infinity, each expression on either side of the subtraction sign approaches 1. That answers the part of convergence/the question.

I know it is convergent, the problem lies within proving it is convergent.

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