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#1 Re: This is Cool » Partial sum formula of a series by recursion » 2017-01-10 01:32:08

I think that i used the wrong word big_smile (I'm italian), with publish i mean post here. However this is my proof:
FluxBB bbcode test
Knowing that:
FluxBB bbcode test  (excuse me the under subscript is 0)
We can rewrite the series so:
FluxBB bbcode test
Now i notice that delta_n appears m-n times in the series:
FluxBB bbcode test
FluxBB bbcode test
FluxBB bbcode test
FluxBB bbcode test
We must work a little more for our formula:
FluxBB bbcode test
QED

#2 Re: This is Cool » Partial sum formula of a series by recursion » 2017-01-09 23:06:48

Well, I never saw the question by this perspective. I think that my formula is simpler because doesn't need the knowledge of bernoulli numbers that are really hard to remember. And if k gets really high my formula is long because of the recursion but still practicable: i challenge everyone at remembering for a long time a big part of Bernoulli sequence. So should i post the proof or it's a naive work?

#3 This is Cool » Partial sum formula of a series by recursion » 2017-01-09 05:57:13

Eulero
Replies: 5

Hi,
I haven't been here for a while, but now i'm back with something new. I found a formula that give the result of the partial sum of the series:
FluxBB bbcode test
For each k positive integer. With recursion i mean: do you want the partial sum formula for n=3? You need to know the partial sum formula for n=2 and for that you need partial sum formula for n=1;etc.
This is the formula:

FluxBB bbcode test

It works perfectly!
Before I publish the proof i really would like your judge:is it a useful formula? Or it's less interesting than i think?
I thank you for every answer.

#5 Re: Puzzles and Games » An interesting equation » 2016-09-15 07:44:26

Good job!
But the fourth solution you proposed is wrong as you can see here. The exercise exalts one of the most curious proprieties of golden ratio : it's the only not integer number whose himself and reciprocal and square have the same fractionary part. When you have time would you post the execution?

#6 Re: Puzzles and Games » An interesting equation » 2016-09-15 03:16:32

It's a solution but not the only one

#8 Puzzles and Games » An interesting equation » 2016-09-15 02:29:47

Eulero
Replies: 17

Hi,
Today I want to propose you a beautiful problem:
Solve the equation:
mant{x^(-1)}=mant{x}=mant{x^2}
Where mant{x} is the mantissa function

#9 Introductions » Hello from Italy! » 2016-09-14 04:42:04

Eulero
Replies: 6

Hello,
I don't know if there are other italian users, I'm here because Italian Math Forums are really boring because of their inactivity. I'm really young (fifteen) but I have a great passion for math and I really like to solve hard problems and puzzles. I'm sorry if my English isn't perfectly correct , but I'll do my best.
smile

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