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8 items are filed under this topic.
Convergent or divergent? 2009-03-03
From Betsy:
Use the ratio test to determine if the series is convergent or divergent. 1+1/2^2+1/3^3+1/4^4

I know the general terms are a(n)=1/n^n and a(n+1)=1/(n+1)^(n+1) but I can't simplify r=lim(n->inf.)=n^n/(n+1)^(n+1)

Answered by Robert Dawson.
Sigma from 0 to infinity of (n^3 / 3^n) 2006-11-15
From Cedric:
I'm wondering how you would find if this series converges or diverges?

Sigma from 0 to infinity of (n^3 / 3^n)

Does the n^3 dominate, or does the 3^n dominate? What about higher powers like n^10 / 10 ^ n ? Which one would dominate then?

Answered by Penny Nom.
A sequence that converges to e 2003-03-16
From Dane:
Something I noticed fooling around with a calculator about 30 years ago.
Considering e = 2.718281828459045....
Using Window's Calculator you will find

1.111 = 2.8531167...
1.01101 = 2.731861...
1.0011001 = 2.71964085...
1.000110001 = 2.71841774...
1.00001100001 = 2.7182954...
1.00000110000011 = 2.178231875...
1.000000110000001 = 2.178219643...

There apears to be a pattern. My conjecture is:

1.'infinite number of zeros'11'infinite number of zeros'1 = e.

Answered by Penny Nom.
Harmonic numbers 2003-03-12
From Becky:
What can you tell me about the limit of harmonic numbers as it reaches infinity?
Answered by Penny Nom.
Power series representations 2000-11-27
From Grace:
Is there a systematic way of finding a power series representation of a function? I understand that you have to manipulate the function so that it is of the form 1/(1-x), but beyond that I am lost.
Answered by Harley Weston.
Radius of convergence 1999-04-21
From Nowl Stave:
Why is the radius of convergence of the first 6 terms of the power series expansion of x^(1/2) centered at 4 less than 6?
Answered by Harley Weston.
A Series 1999-04-20
From Deepak Shrestha:
Given the sequence an=e^(-n*Ln(n)), does the series converge and why?
Answered by Harley Weston.
Neighbourhoods 1996-02-14
From Robert:
What are neighbourhoods?
Answered by Harley Weston.



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