General Summations

n
i=1
G(i) = G(n + 2) – G(2) Vajda-33, Dunlap-38
n
G(i) = G(n + 2) – G(a + 1) -
Fibonacci and Golden Ratio Equations http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibForm...
10 of 12 6/4/03 1:49 PM
i=a
n
i=1
G(2 i – 1) = G(2 n) – G(0) Vajda-34, Dunlap-37
n
i=1
G(2 i) = G(2 n + 1) – G(1) Vajda-35, Dunlap-39
n
i=1
G(2 i) –
n
i=1
G(2 i – 1) = G(2 n – 1) + G(0) – G(1) Vajda-36, Dunlap-40
n
i=1
2n – i G(i – 1) = 2n – 1( G(0) + G(3) ) – G(n + 2) Vajda-37(variant), Dunlap-41(variant)
4 n + 2
i=1
G(i) = L(2 n + 1) G(2 n + 3) Vajda-38, Dunlap-43
2 n
i=1
G(i) G(i – 1) = G(2 n)2 – G(0)2 Vajda-39, Dunlap-44
2 n +
1
i=1
G(i) G(i – 1) = G(2 n + 1)2 – G(0)2 – G(1)2 +
G(0) G(2) Vajda-41, Dunlap-46
n
i=1
G(i + 2) G(i – 1) = G(n + 1)2 – G(1)2 Vajda-43, Dunlap-48
n
i=1
G(i)2 = G(n) G(n + 1) – G(0) G(1) Vajda-44, Dunlap-49
i = 0
G(a, b, i)
ri
a + b r
= a +
r2 – r – 1
Stan Rabinowitz,
"Second-Order Linear Recurrences"
card,
Generating Function
special case (x=1/r, P=1, Q=-1)
i = 0
i G(a, b, i)
ri
r (b r2 – 2 a r + b – a)
=
(r2 – r – 1)2 -
n
i = 1
n – i
i – 1
= F(n) -
Fibonacci and Golden Ratio Equations http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibForm...
11 of 12 6/4/03 1:49 PM
i = 0
n – i – 1
i = F(n) Vajda-54(corrected), Dunlap-84(corrected)
n
i = 0
n + 1
i + 1 F(i) = F(2 n + 1) – 1 Vajda-50, Dunlap-82
2 n
i = 0
2 n
i F(2 i) = 5n F(2 n) Vajda-69, Dunlap-85
2 n
i = 0
2 n
i L(2 i) = 5n L(2 n) Vajda-71, Dunlap-87
2 n + 1
i = 0
2 n + 1
i F(2 i) = 5n L(2 n + 1) Vajda-70, Dunlap-86
2 n + 1
i = 0
2 n + 1
i L(2 i) = 5n + 1 F(2 n + 1) Vajda-72, Dunlap-88
2 n
i = 0
2 n
i F(i)2 = 5n – 1 L(2 n) Vajda-73, Dunlap-89
2 n
i = 0
2 n
i L(i)2 = 5n L(2 n) Vajda-75, Dunlap-91
2 n + 1
i = 0
2 n + 1
i F(i)2 = 5n F(2 n + 1) Vajda-74, Dunlap-90
2 n + 1
i = 0
2 n + 1
i L(i)2 = 5n + 1 F(2 n + 1) Vajda-76, Dunlap-92
i=0
5i n
2 i + 1 = 2n-1 F(n) Vajda-91
5i n
2 i = 2n-1 L(n) Vajda-92
Fibonacci and Golden Ratio Equations http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibForm...
12 of 12 6/4/03 1:49 PM
i=0
With Generalised Fibonacci
n
i = 0
ni
G(i) = G(2 n) Vajda-47, Dunlap-80
n
i = 0
ni
G(p – i) = G(p + n) Vajda-46, Dunlap-79
n
i = 0
n
i
G(p + i) = G(p + 2 n) Vajda-49, Dunlap-81
n
i = 0
(–1)i n
i G(n + p – i) = G(p – n) Vajda-51, Dunlap-83

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the Inverted Hammer

As Forexgen Presents the Inverted Hammer is a pattern that occurs at the bottom of a downtrend. It indicates a possibility of the reversal of the downtrend.

Recognition Criteria:

• A small real body is near the lower part of the price range.
• The very long upper shadow.
• Occurs in a downtrend.

Also The Shooting Star is a bearish reversal pattern. It occurs in an upper trend which indicates that the market opens at the lows of the season, rallies and pulls back to the bottom.

Recognition Criteria:

• A very long upper shadow.
• The small real body at the lower end of the price range.
The real body gaps away from the prior real body.

Consumers cut spending

Consumers cut spending during October at the steepest rate in more than seven years and orders for costly manufactured goods plummeted, according to Commerce Department reports on Wednesday that implied a steep recessionary downturn was at hand.
Spending that fuels two-thirds of U.S. economic activity dropped 1.0 percent, its biggest fall since the attacks against the United States seven years ago in September 2001.

It was a fourth straight monthly fall in spending and underlined how a credit crunch, falling home prices and steady job losses were sapping consumers' will and ability to spend.

Worse yet, a survey showed consumer confidence fell to a 28-year low in November as mounting job losses, falling incomes and tumbling household wealth battered sentiment, highlighting the troubles for the economy ahead.

Orders for costly durable goods like cars, machinery and computers dropped by 6.2 percent in October, more than twice as much as Wall Street economists had forecast, as demand weakened across nearly every major sector of manufacturing.

read more....

http://biz.yahoo.com/rb/081126/business_us_usa_economy.html?.v=6