** Please see the attachment for the complete problem description **
iv) Series C and S are defined as follows:
C=2cos x + 4 cos 2x + 8 cos 3x + ... + 2^n cos nx
S=2 sin x + 4 sin 2x + 8 sin 3x + ... + 2^n sin nx
Show that C+iS is a geometric series. Hence show that:
S= 2sin x - 2^n+1 sin ((n+1)x) + 2^n+2 sin nx /

GeometricMean (example question)
The prices of five computer stocks increased by 37.2 %, 1,140.0 %, 2.7 %, 842.0% and 0.95 %, respectively since 1990. Compute the geometricmeanrate of return for the five stocks.
(Hint: First convert percents to decimal equivalent)

Please define and describe the difference between arithmetic average versus geometric average. Which one is more effective or provides a more complete picture when valuing a stock's past performance over the last 5 years?

A geometric progression has first term log_2 27 and common ratio log_2 y, find the set of values of y for which the geometric progression has a sum to infinity.
My logic:
If sum to infinity exists then 1- log_2 y > 0
- log_2 y > -1
log_2 y < 1
y< 2^1
y< 2
Where next?

1. According to the Census:
http://www.census.gov/compendia/statab/cats/banking_finance_insurance/payment_systems_consum
er_credit_mortgage_debt.html
The amount of consumer credit outstanding (in billions of dollars) for selected years is as follows:
1998: $1,421
2003: $2,078
2008: $2,563
a. Find the geometric mea

Stock XYZ (end of the year values)
2003 2004 2005 2006 2007
Stock Price $20.50 $24.00 $36.25 $43.00 $56.50
Dividends $0.23 $0.23 $0.25 $0.27 $0.31
1. Calculate the compound annual rate of return on the stock investment.
2. For the dividends, calculate the a-ari

A recent article suggested that if you earn $25,000 a year today and the inflation rate continues at 3 percent per year, you'll need to make $33,598 in 10 years to have the same buying power. You would need to make $44,771 if the inflation rate jumped to 6 percent.
Confirm that these statements are accurate by finding the geo