How do you determine if the series the converges conditionally, absolutely or diverges given #Sigma ((-1)^(n+1)n^2)/(n+1)^2# from #[1,oo)#?

Question

How do you determine if the series the converges conditionally, absolutely or diverges given #Sigma ((-1)^(n+1)n^2)/(n+1)^2# from #[1,oo)#?

1 Answer

Impact of this question

1579 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-03T22:08:01

The series diverges.

Explanation:

The series #sum_(n=1)^oo(-1)^(n+1)n^2/(n+1)^2# is made up of two parts.

The #(-1)^(n+1)# part alternates between #1# and #-1#, only changing the sign of each term.

The meat of the sequence is #n^2/(n+1)^2#. Note that #lim_(nrarroo)n^2/(n+1)^2=1#.

So, as the series extends infinitely, alternating terms approaching a value of #1# are continually being added and subtracted, so the series never converges.

Science

Math

Humanities

... and beyond

How do you determine if the series the converges conditionally, absolutely or diverges given #Sigma ((-1)^(n+1)n^2)/(n+1)^2# from #[1,oo)#?

1 Answer

Explanation:

Related questions

Impact of this question