8.2. GEOMETRIC SERIES
457
(f) Complete Table 8.2 with values of Q(n) for the provided n-values (reporting Q(n)
to 10 decimal places). What appears to be happening to the sequence Q(n) as n
increases?
Q(1) 0.40
Q(2)
Q(3)
Q(4)
Q(5)
Q(6)
Q(7)
Q(8)
Q(9)
Q(10)
Table 8.2: Values of Q(n) for selected values of n
⊲⊳
Geometric Sums
In Preview Activity 8.2 we encountered the sum
(5 × 0.08)
1 + 0.08 + 0.08
2 + 0.08
3 + · · · + 0.08
n−1
.
In order to evaluate the long-term level of Warfarin in the patient’s system, we will want to
fully understand the sum in this expression. This sum has the form
a + ar + ar
2 + · · · + ar
n−1
(8.1)
where a = 5 × 0.08 and r = 0.08. Such a sum is called a geometric sum with ratio r. We
will analyze this sum in more detail in the next activity.
Activity 8.4.
Let a and r be real numbers (with r 1) and let
S n = a + ar + ar
2 + · · · + ar
n−1 .
457
(f) Complete Table 8.2 with values of Q(n) for the provided n-values (reporting Q(n)
to 10 decimal places). What appears to be happening to the sequence Q(n) as n
increases?
Q(1) 0.40
Q(2)
Q(3)
Q(4)
Q(5)
Q(6)
Q(7)
Q(8)
Q(9)
Q(10)
Table 8.2: Values of Q(n) for selected values of n
⊲⊳
Geometric Sums
In Preview Activity 8.2 we encountered the sum
(5 × 0.08)
1 + 0.08 + 0.08
2 + 0.08
3 + · · · + 0.08
n−1
.
In order to evaluate the long-term level of Warfarin in the patient’s system, we will want to
fully understand the sum in this expression. This sum has the form
a + ar + ar
2 + · · · + ar
n−1
(8.1)
where a = 5 × 0.08 and r = 0.08. Such a sum is called a geometric sum with ratio r. We
will analyze this sum in more detail in the next activity.
Activity 8.4.
Let a and r be real numbers (with r 1) and let
S n = a + ar + ar
2 + · · · + ar
n−1 .