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:
Step-by-step explanation:
<u>Given:</u>
<u>Rewrite it as:</u>
<u>Simplify the expression:</u>
Find the inverse of that function:
y = e^x
Answer:
multiplying both-side of the equation by 3
substituting 36 for p to check the solution
Step-by-step explanation:
To solve the equation p/3 = 12, we will follow the steps below;
first multiply 3 to both-side of the equation, that is:
p/3 × 3 = 12 × 3
On the left-hand side of the equation, 3 at the numerator will cancel-out 3 at the denominator, leaving us with just p while on the right-hand side of the equation 12 will be multiplied by 3
p= 36
To check the correctness of the equation, we can substitute p = 36 back into the equation and then check, that is;
p/3 = 12
36/3 = 12
This implies p = 36 is correct
Answer:If she buys 60 tiles, the cost at both shops is the same.
If she buys less than 60 tiles, then the second shop is cheaper.
If she buys more than 60 tiles, then the first shop is cheaper.
Step-by-step explanation:
Explanation:
Let the number of tiles be
x
At the first shop: Cost =
$
0.79
×
x
+
$
24
=
0.79
x
+
24
At the second shop: Cost =
$
1.19
×
x
=
1.19
x
If the cost is the same:
1.19
x
=
0.79
x
+
24
←
solve for x
1.19
x
−
0.79
x
=
24
0.4
x
=
24
x
=
24
0.4
x
=
60
tiles
If she buys less than 60 tiles, then the second shop is cheaper.
If she buys more than 60 tiles, then the first shop is cheaper.
