Math Is Fun Forum

MisterMaths

Member

Registered: 2017-05-13

Posts: 2

I need some help with this.

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=

iamaditya

Member

From: Planet Mars

Registered: 2016-11-15

Posts: 821

Re: I need some help with this.

I think it is divergent.

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greg1313

Member

Registered: 2016-12-19

Posts: 20

Re: I need some help with this.

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.)

MisterMaths

Member

Registered: 2017-05-13

Posts: 2

Re: I need some help with this.

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.