Answer:
Given the series,
∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1
I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)
So,
∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞
There are different types of test to show if a series converges or diverges
So, using Ratio test
Lim n → ∞ (a_n+1 / a_n)
Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))
Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))
Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)
Lim n→ ∞ (-1/2)^(n-n+1)
Lim n→ ∞ (-1/2)^1 = -1/2
Since the limit is less than 0, then, the series converge...
Sum to infinity
Using geometric progression formula
S∞ = a / 1 - r
Where
a is first term
r is common ratio
So, first term is
a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1
a_1 = -4
Common ratio r = a_2 / a_1
a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2
a_2 = 2
Then,
r = a_2 / a_1 = 2 / -4 = -½
S∞ = -4 / 1--½
S∞ = -4 / 1 + ½
S∞ = -4 / 3/2 = -4 × 2 / 3
S∞ = -8 / 3 = -2⅔
The sum to infinity is -2.67 or -2⅔
<h2>
Step-by-step explanation: PHEW THAT TOOK A WHILE LOL IM A FAST TYPER</h2>
Check all options:
A. The notion 
represents the line YX. As you can see the line YX is present in the diagram.
B. Start with point Z, go to the point X and then to the point Y. You path is along ∠ZXY sides, this means that you can see ∠ZXY on the picture.
C. The notion 
represents the ray ZX. On the picture is given segment ZX, not ray, then this option is false.
D. To form the ∠XYZ you have to connect points Z and Y. Without this connection ∠XYZ cannot be seen. This option is false.
Answer: True options are A and B.
Yes, a right triangle can be an isosceles triangle sometimes.
C.
An isosceles triangle is a triangle with two or more sides of the same length. A right triangle is a triangle that has a right angle, therefore it is possible to have a right isosceles triangle.
Answer:
c) It can be equal to 1.00 but it can also be greater than 1.00. It is never less than 1.00.
Explanation:
Refractive index is equal to velocity of the light 'c' in empty space divided by the velocity 'v' in the substance.
Or ,
n = c/v.
Since speed of the light 'v' in any medium is always be less than or equal to speed of the light in the vacuum 'c', thus, the index of refraction is always be greater than or equal to 1.0.
Step-by-step explanation:
One piece of paper is 44 and the other is 33
she can cut each strip where it is 11 inches in width
