Math Is Fun Forum

enita

Guest

series2

sorry to bother you again!

I need help with two questions on series..

1. Find the range of values for which the following series is convergent or divergent:

2. Investigate the convergence of the series

for

Hope you can help. Thanks

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: series2

#2.)  This was really hard for my BASIC program I wrote because of rounding errors.
The best I could come up with is that at 0.9999, you get 10.34 or something.
And at 0.99995 it started to grow, so maybe that means at 1 it goes to infinity.
If I have time, I'll try to program this with a better precision program.  Sorry.
So the answer just might be convergence of 10.33 at about .999999, not sure...

---

igloo myrtilles fourmis

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: series2

1) |x|<1 convergent, |x|>1 divergent-an 1.0001^n series go larger and larger than n^3 series sooner or later. x=1 or x=-1 case, by evaluating them in the series formula we know convergence.
So the convergence interval is [-1,1]

---

X'(y-Xβ)=0

enita

Guest

Re: series2

thanks for your replys guys

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: series2

2. John, you're right.
for |x|<=1 the second coverages, and it's:

Last edited by krassi_holmz (2007-02-03 21:55:58)

---

IPBLE:  Increasing Performance By Lowering Expectations.