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
Given:
32 and 28 are the two numbers.
To find:
(a) The GCF of 32 and 28.
(b) Using the GCF, find the factor of (32-28).
Solution:
(a)
The factor forms of the given numbers are:
It is clear that, 2 and 2 are the common factors in both.
Hence, the GCF of 32 and 28 is 4.
(b)
Using the GCF we need to find the factor of (32-28).
Taking out the GCF, we get
Hence, .
3 miles, because if you think of it like a box, a box has to have 4 sides, you know that there are 2 sets of sides, a set that will be the size of the length and a set that will be the size of the width, so you multiply the width by 2 then multiply the length by 2 and add them
1*2 = 2
.5 * 2 =1
2+1 = 3
Mark up value is either a fixed amount or a percentage of the total cost or selling price.
In this problem, mark up value is the percentage of the total cost.
To determine the retail price, total cost and mark up must be added.
Selling Price = Total Cost + Mark up value based on Total Cost
However, we are looking for the Total cost. Thus, our formula should be
Total Cost = Selling Price - Mark up value based on Total Cost.
Let X = total cost.
Selling Price = $8,000
Mark up vale = 6% of total cost.
X = $8,000 - 6%X
X = $8,000 - 0.06X
To get X, transfer -0.06X to the other side and change its sign from negative to positive.
X + 0.06X = $8000
1.06X = $8000
To get X, divide both sides by 1.06
1.06X / 1.06 = $8000 / 1.06
X = $7,547.17 total cost.
The problem is looking for the mark up value and since it states that the mark up value is 6% of the total cost, then:
Total Cost x 6% = Mark up value
$7,547.17 x 0.06 = $452.83 mark up value
To check:
X + 0.06X = $8000
$7547.17 + $452.83 = $8000
$8000 = $8000 equal.