Register to reply

Help with Series Problem

by Fresh(2^)
Tags: help with series, series
Share this thread:
Fresh(2^)
#1
Apr20-10, 05:53 AM
P: 5
1. The problem statement, all variables and given/known data

Not expected to do for Home work but i found the problem interesting. The problem is exactly as stated in Att.


2. Relevant equations

Not sure:: d = C/pi?



3. The attempt at a solution

Really I don't see a systematic way of approaching this problem, but these are the ideas ! have: Notice that the limit of the of the partial sums must be = 1 ( for n = 1 to infinity; n n--> inf.) which is the radius of the outer circles. So Cn :: the expression to be found is convergent. Here also C1 > C2. 0 < Cn < Cn - 1 < 1. that lets me consider 1 > 1/(n + 1). which encourages .. 1 - 1/ (n +1) as the partial sum taking the lim n --> to inf. i get 1 then adding i get 1/n(n+1) for diameter of Cn Is this reasoning correct ? If not I'd appreciate a prod in right direction.

thanks guys
-Orson
*for some reason Att, is showing up, I used the upload from computer tool but i don't see the attachment. ohh my bad
Attached Thumbnails
PRobLEm_^3_PF_help.jpg  
Phys.Org News Partner Science news on Phys.org
World's largest solar boat on Greek prehistoric mission
Google searches hold key to future market crashes
Mineral magic? Common mineral capable of making and breaking bonds
Filip Larsen
#2
Apr24-10, 12:20 PM
PF Gold
Filip Larsen's Avatar
P: 958
I'm not sure I understand your idea so I am not able to tell if the will be productive or not. However, I do know that you can solve the problem by looking at the geometric relationship between height (above bottom line) and radius of Cn (hint: use Pythagoras) and then build a recursive definition of these knowing the height of C1 is 0 and solve some finite sums. Its actually quite interesting how the radius comes out rather simple in the end.


Register to reply

Related Discussions
Series problem Calculus & Beyond Homework 7
HARD problem on mathematical problem and fourier series Math & Science Software 0
Another Series problem Calculus & Beyond Homework 3
Problem with a sum of series General Math 2
Series problem Calculus 4