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.
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.
.....(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: