Help With sequences and series.

Dec 2016
2
0
Morocco
Forgive me if this is the wrong section for this, but I study maths in French.
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 some things might not make sense since they are directly translated by me, but after all maths is one language.

I want to determine whether this sequence is convergent or divergent: Un=
 
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Country Boy

Math Team
Jan 2015
3,261
899
Alabama
Forgive me if this is the wrong section for this, but I study maths in French.
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 some things might not make sense since they are directly translated by me, but after all maths is one language.

I want to determine whether this sequence is convergent or divergent: Un=
Use the general formula \(\displaystyle x^n- y^n= (x- y)(x^{n-1}+ x^{n-2}y+ \cdot\cdot\cdot+ xy^{n-2}+ y^{n-1})\) with \(\displaystyle x= \sqrt[n]{n+1}\) and \(\displaystyle y= \sqrt[n]{n}\).
 
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May 2017
7
0
south korea
if you have a hard time to understand County Boy's suggestion, then consider few things

1. second parenthesis is collection of terms in a form of i x^(n-a) * y ^(a-1) when a is from 1 to n

2. general expression T(a) = x^n-a * y^(a-1) suffice certain conditions in the cases
x^(n-1) < T(a) < y^(n-1)

3. so second term is within n* x^(n-1) and n* y^(n-1)
 
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