Re: twin prime conjecture

In article <1160567009.355920.117830@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"larry.freeman@xxxxxxxxx" <larry.freeman@xxxxxxxxx> wrote:

OK, here's the solution to one more of your problems (2 more to go):

1. Prove that F_1 + F_2 + F_3 + ... + F_n = F_(n + 2) - 1

(a) F(4) - 1 = F(3) + F(2) - 1 = F(2) + F(1) + F(2) - 1 = F(2) + F(2)
= F(2) + F(1) + F(0) = F(2) + F(1)

(b) Assume that this is true up to n so that:

F(n) - 1 = F(n-2) + ... + F(1)

(c) Then F(n+1) - 1 = F(n) + F(n-1) - 1

(d) Applying (b) gives us:

F(n+1) - 1 = F(n-1) + F(n-2) + ... F(1)

(e) Using mathematical induction, we are done.

QED

OK. But you can stop now - you've made your point
(unless of course you're enjoying this, in which case,
be my guest).

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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