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
Answer:
Step-by-step explanation:
Each year, the plant earns an additional 5 percent per man-hour. This means that the increase in earnings is exponential. We would apply the formula for exponential growth which is expressed as
A = P(1 + r)^t
Where
A represents the amount earned after t years.
t represents the number of years.
P represents the initial amount earned.
r represents rate of growth.
From the information given,
P = $800
r = 5% = 5/100 = 0.05
Therefore, the function that gives the amount after t years is
A = 800(1 + 0.05)^t
A = 800(1.05)^t
Point c.
You can graph the two points in a calculator to find out the answer OR you can identify the lines using the y-intercept aka b in the y=mx+b format.
Y=x - 3 has a y-intercept of -3, so look for the line where it goes through -3 on the y axis. (do the same for the other except when the y-intercept is 1)
From this, you can identify the lines and just find where they intersect.
Answer:
8/9
Step-by-step explanation:
3/6 + 7/ 18
Make the denominator common by finding the LCM = 18
Multiply 3 by 3
Therefore sum = 3*3 + 7/ 18
sum = 9+7/18
sum = 16/18
=> 8/9
Please mark my answer as the brainliest for further answers :)