Can you solve this series?

Fistfiz · 2012-07-20 22:27:27

Hi guys, can you help me with this? (i'm sorry, i don't know how to write in code, maybe a mod can edit this :-) )

∑ (from k=1 to j) of : m/(m+1-k)

can you find a general formula for this series?

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OT:
The problem which led me to this other problem is this:

I have a bag with 100 blue balls;
to do one exchange means to take one random ball from the bag and put a red ball in;
how many average exchange does it take to have 50 red balls in the bag??

my reasoning is:
the average number of exchanges to add a red ball is given by

n=1/P, where P is the probability of taking a blue ball from the bag (P=#blueballs/#allballs)
since a missed tentative does not affect the number of blue balls in the bag, our number of exchanges is given by:

n=1+100/99+100/98+...+100/51 that you can obtain from the series above by putting m=100 and j=50

what do you think about it?

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sorry for the english, i'm from Italy... hope i've made it clear

bobbym · 2012-07-21 00:21:19

Hi;

The series has a closed form but not in terms of elementary functions.

But in my opinion this is not correct.

what do you think about it?

Your solution to the urn problem holds up to my simulations.

Fistfiz · 2012-07-21 04:28:15

Thanks :-)
Unfortunately I have no idea of what that psi function is...
What do you think is not correct? My solution to the original problem or your closed form?

bobbym · 2012-07-21 04:45:47

That closed form is gibberish. Amazingly both Mathematica and Maple get it!

Your solution to the urn problem does appear to work.

Math Is Fun Forum

#1 2012-07-20 22:27:27

Can you solve this series?

#2 2012-07-21 00:21:19

Re: Can you solve this series?

#3 2012-07-21 04:28:15

Re: Can you solve this series?

#4 2012-07-21 04:45:47

Re: Can you solve this series?

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