Answer:
The series is absolutely convergent.
Step-by-step explanation:
By ratio test, we find the limit as n approaches infinity of
|[a_(n+1)]/a_n|
a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)
a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)
[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]
= |-3n³/2(n+1)³|
= 3n³/2(n+1)³
= (3/2)[1/(1 + 1/n)³]
Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity
= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity
= 3/2 × 1
= 3/2
The series is therefore, absolutely convergent, and the limit is 3/2
Step-by-step explanation:
You need to find 7 1/2% of $29.95.
To do that, just multiply the percent by the number.
7 1/2% * $29.95 =
= 7.5% * $29.95
= 0.075 * $29.95
= $2.24625
The answer is $2.25
Answer:
D. The mean will shift to the left.
Because if they sell lower priced cars it will bring the average price down causing the mean to move to the left
d = r * t
d/t = r
-35.75 / 3.25 = r
-11 = r
r = -11 ft / min
d = r*t
d = -11 ft/min * 1 min
d = -11 ft
The probe is 11 feet below sea level after 1 minute
