Answer:
The series converges.
Step-by-step explanation:
According to the alternating series test:
For a series ∑(-1)ⁿ aₙ or ∑(-1)ⁿ⁺¹ aₙ
If lim(n→∞) aₙ = 0
and aₙ is decreasing,
then the series converges.
aₙ = n² / (n³ + 1)
Since the power of the numerator is less than the power of the denominator, lim(n→∞) aₙ = 0.
Since n² / (n³ + 1) > (n+1)² / ((n+1)³ + 1), the series is decreasing. (We could also prove this by showing that the derivative is negative.)
Therefore, the series converges.
Answer:
slope 3
Step-by-step explanation:
-2+y=4
4+y=10
10+y=16
y= 6
0+x=2
2+x=4
4+x=6
x=2
slope= change in y/ change in x
6/2=3
Rectangle=21 times 14=294 cm^2
Triangle=Base Times Height
Height=21-12=9cm
Area of triangle=16 times 9 =144
Area of both=294+144=438cm^2
Answer:
The table is attached as a figure
The given equation is ⇒⇒⇒⇒ y = 2x
To solve this equation, we need to pick numbers from the table then this number will be substituted into the equation to find y
we need 3 solutions . so, we need to pick 3 numbers of x
From the table, let us choose x = 0
y = 2x
y = 2 * (0)
y = 0
From the table, let choose second value of x such as x = 1
y = 2 * (1)
y = 2
From the table, let choose third value of x such as x = -1
y = 2 * (-1)
y = -2
So, the picked three solutions are
y = 0 at x = 0
y = -2 at x = -1
y = 2 at x = 1
Answer:
A=8
B=45
C=18
I did the assignment and got the question right.