Either I don't know what "p" is or that just makes no sense. That's an awful lot of unrelated irrational numbers magically adding up to a Rational.

There must be a typo or simply proving it incorrect is easy enough.

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- August 13th 2008, 12:59 PM #1

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- August 13th 2008, 01:24 PM #2

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- August 13th 2008, 01:42 PM #3
What's that p doing there .. I'm guessing it should be an 'n'. In any case, this sounds like a proof by induction.

Let be the statement that .

Base case: P(1): 0 = 0. True.

Inductive step: Assume to be true. [tex] We must show that is also true, i.e.

Looking at the left hand side (LHS)

We see that and the next integer up would be . So, since our last term is (one less), then we see that :

Now, rewriting the equation and noticing that what is in red is

Now hopefully if you simplify it, you'll get what you want.

Phew!

- August 13th 2008, 03:41 PM #4

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- August 14th 2008, 02:49 AM #5

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- August 14th 2008, 04:27 AM #6

- August 14th 2008, 06:29 AM #7

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yes i undetsand what he wrote.it's more simple than :

.....(what i wrote)

But in my demonstration(in the book)they are not precise anything of that

they write directly the solution .

i thought that :

have a special proprities,for this reason i ask you again:

have ...a special proprities???

for the exemple:

how we can sum that: