Mohammad Hammad
New member
- Joined
- Jul 11, 2019
- Messages
- 38
it's an infinite series but you can stop at any point you want to have a set of fractions from one given fraction.You already started a thread for this, so it might make sense if you post your correction in the other thread(click) and abandon this one (perhaps a moderator will delete this thread)
FYI: It looks correct to me. Do you have a use in mind for it?
I have two comments.
First, I would call this a derivation, rather than a proof. A proper proof might use induction, using the same ideas you show here.
Second, you say nothing about convergence. Without that, this can't really be called true or false. When does it converge? Where is the proof?
But you mentioned a proof. Not a demonstration.if you try wolfram.com you will get that this infinite series have a convergence always except for x=0
it's from this oneif we take the second parameter divided by first parameter:
View attachment 29351
Lim (1!/((x+1)(x+2)))/(0!/(x+1))
= Lim (1/(x+2)). which is less than 1 for all positive integers .
is this a fair proof that this series is converges ?!
I understand that you can turn a fraction into an exactly equivalent sum of fractions, but do you have a use in mind for this? Or, perhaps, this is just an interest of yours (which is absolutely fine)?it's an infinite series but you can stop at any point you want to have a set of fractions from one given fraction.
for example
1/4=1/5+ 1/20. for 2 fractions. or
1/4=1/5+ 1/30+ 1/60. for 3 fractions or
1/4= 1/5 +1/30+1/105+1/140. for 4 fractions.
and you can get whatever numbers of fractions from 1/4.