You are not logged in.
#3 2009-04-25 20:44:01
- mathsyperson
- Moderator
Offline
Re: find sum
I think it's just a +4, +2, ... pattern on the denominator.
I haven't solved it yet, but it's fairly easy to see that it's somewhere between 0.8 and 1.
Why did the vector cross the road?
It wanted to be normal.
#4 2009-04-25 21:45:57
- JaneFairfax
- Legendary Member
Offline
Re: find sum
tony123 wrote:
You made a little mistake, mate. I think you want to find
The Maclaurin series for is
Also
Hence
#5 2009-04-26 03:53:15
- tony123
- Full Member
Offline
Re: find sum
JaneFairfax wrote:
tony123 wrote:
You made a little mistake, mate. I think you want to find
no jane
#6 2009-04-26 04:19:38
- JaneFairfax
- Legendary Member
Offline
Re: find sum
Then you should have been more clear in the first place. 
#7 2009-04-29 01:49:30
- bobbym
- Administrator
Offline
Re: find sum
Hi Tony123;
Start by forming the power series:
This will equal the terms of Tony's series if x=1. There are differences of 4 and 2 in the exponents. The expansion:
Has exponents that differ by 2.
Has exponents that differ by 4. To get differences of 4 and 2 we use a
This has the required differences of 4 then 2 in the exponents.
Now I tried to use integration, differentiation or multiplication by x on (B)
to make it look like series (A).
I couldn't. So I tried
This one doesn't have the required 4,2 difference in the exponents so it can't be right.
When I tried:
This looks good. Integrate this series and you get
(C) is series (A). So we have:
Now we need the integral.
with x=1
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#9 2009-04-29 11:58:10
- bobbym
- Administrator
Offline
Re: find sum
Thanks for posing it. It was really a tough problem.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#10 2011-07-30 02:28:09
- gAr
- Star Member
Offline
Re: find sum
Hi,
My method may be the same what bobbym says, but I approached by observing that the series is
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
#11 2011-10-07 19:41:45
- SeireeIngemia
- Banned
Offline
Re: find sum
My friend showed me this one the other day and I thought it was fun.
1
11
21
1211
111221
-->What goes here?
Hope its not too easy
#12 2011-10-07 20:39:34
- bobbym
- Administrator
Offline
Re: find sum
Hi SeireeIngemia;
Please start a new thread instead of tacking on to an earlier question for new problems. That way they get the attention they deserve.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#13 2011-10-08 00:10:41
- anonimnystefy
- Real Member
Online
Re: find sum
the next element is 312211
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón