Topic: converge list of topics
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8 items are filed under this topic.

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	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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