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`Wtf is this series

Blogs > EtherealDeath
Post a Reply
EtherealDeath
Profile Blog Joined July 2007
United States8366 Posts
January 22 2009 16:31 GMT
#1
1.4142 – .7071 + .5303 – .4419 + .3867 – .3480 + .3190 – .2962 + …

eh....

So the first term is approximately sqrt(2), the second term 1/2 of that, then the third term i have no clue wtf is going on....and it goes downhill from there.

It was a specific example they gave for the problem:

Investigate a formula in Finite Differences for transforming a series the terms of
which (at least after a certain number) are alternately positive and negative, and decrease
slowly, into one which is generally much more rapidly convergent.

But yea, currently preoccupied with that series...don't really recognize wtf it's doing. Unless there really is no pattern to it..but that would suck. Though the main problem itself is somewhat interesting too.

emperorchampion
Profile Blog Joined December 2008
Canada9496 Posts
January 22 2009 16:58 GMT
#2
ok so the the pattern seems to be n, 1/2, 3/4, 5/6, 7/8, 9/10, 11/12, 13/14

so as I saw add 1/2, n+1/2, n-3/4, ect.
lol i need to go now

TRUEESPORTS || your days as a respected member of team liquid are over
Physician *
Profile Blog Joined January 2004
United States4146 Posts
Last Edited: 2009-01-22 17:02:53
January 22 2009 17:01 GMT
#3
Smith's Prize Exam, taken by James Clerk Maxwell at Cambridge, Feb 1854: Question 8 on Stokes' Theorem. - google o_Oa!! (it doesn't exactly answer ur question but now u know were they got it from!)
"I have beheld the births of negative-suns and borne witness to the entropy of entire realities...."
Nytefish
Profile Blog Joined December 2007
United Kingdom4282 Posts
January 22 2009 17:06 GMT
#4
sqrt2, 1/2 * sqrt 2, 1/2 * 3/4 * sqrt 2, 1/2 * 3/4 * 5/6 sqrt 2, 1/2 * 3/4 * 5/6 * 7/8 sqrt 2
No I'm never serious.
EtherealDeath
Profile Blog Joined July 2007
United States8366 Posts
January 22 2009 17:23 GMT
#5
oh damn lol
EtherealDeath
Profile Blog Joined July 2007
United States8366 Posts
Last Edited: 2009-01-22 17:25:03
January 22 2009 17:24 GMT
#6
i guess those 1/2 -> 3/4 -> 5/6 change the value faster than i thought
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