Not an expertise on infinite sums but the most straightforward explanation is that infinity isn't a number.
Let's see if there are anything we missed:
∞
Σ 2^n=1+2+4+8+16+...
n=0
We multiply (2-1) on both sides:
∞
(2-1) Σ 2^n=(2-1)1+2+4+8+16+...
n=0
And we expand;
∞
Σ 2^n=(2+4+8+16+32+...)-(1+2+4+8+16+...)
n=0
But now, imagine that the expression 1+2+4+8+16+... have the last term of 2^n, where n is infinity, then the expression of 2+4+8+16+32+... must have the last term of 2(2^n), then if we cancel out the term, we are still missing one more term to write:
∞
Σ 2^n=-1+2(2^n)
n=0
If n is infinity, then 2^n must also be infinity. So technically, this goes back to infinity.
Although we set a finite term for both expressions, the further we list the terms, they will sooner or later approach infinity.
Yep, this shows how weird the infinity sign is.
Answer:
(-7, -3) (Answer A)
Step-by-step explanation:
We start with the point (-7, -3). The x-coordinate does not change at all if we reflect this point across the x-axis. Whereas the y-value of (-7, -3) is -3, we end up with +3 after this reflection. The desired image is (-7, +3) (Answer A)
Answer:
A,B,D
Step-by-step explanation:
Answer:
x=34
Step-by-step explanation:
6 - ( x-7) ^ 1/3 = 3
Subtract 6 from each side
6-6 - ( x-7) ^ 1/3 = 3-6
- ( x-7) ^ 1/3 = -3
Divide each side by a negative
( x-7) ^ 1/3 = 3
Cube each side
( x-7) ^ 1/3 ^3 = (3)^3
x-7 = 27
Add 7 to each side
x-7+7 = 27+7
x = 34
Check
6 - ( 34-7) ^ 1/3 = 3
6 - (27^1/3 = 3
6 -3 =3
3=3
Good solution
Answer:
See attachment for rectangle
Step-by-step explanation:
Given
Required
Draw the rectangle
First, we calculate the distance between A and B using distance formula;
So, we have:
The above represents the length of the triangle.
Next, calculate the width using:
Divide both sides by 2
This implies that, the width of the rectangle is 6 units.
We have:
Since A and B are at the upper left and right, then the ther two points are below.
6 units below each of the above point are:
=> 
=> 
Hence, the points of the rectangle are:
<em>See attachment for rectangle</em>
