Question 26075
Use the geometric series of numbers 1, 1/2, 1/4, 1/8,…to find the following:
a)	What is r, the ratio between 2 consecutive terms? 
R=(1/2)/1=1/2...IT IS SAME FOR ANY 2 CONSECUTIVE TERMS...SAY
(1/8)/(1/4)=1/2...ETC......

b)	Using the formula for the nth term of a geometric series, what is 10th term?
TN=A*(R)^(N-1)=1*(1/2)^(N-1)
T10=(1/2)^(10-1)=(1/2)^9	 

c)	Using the formula for the nth term of a geometric series, what is 12th term?	
T12=(1/2)^11

d)	What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?	

THE NUMBERS TEND TO ZERO AS N INCREASES TO LARGE NUMBERS AND TOWARDS INFINITY.
SUM OF A G.P. TO INFINITE TERMS WITH R<1 IS GIVEN BY 
A/(1-R)=1/(1-0.5)=2