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>
4k(3c-10)
factoring:
14ck *2 + 10ck *2 - 16ck - 40k
28ck -16ck - 40k
12ck - 40k
Step-by-step explanation:
5²=4²+x²
25=16+x²
25-16=x²
9=x²
√9=√x²
3=x
A
For y=2x+125, the slope is 2, which means that the total will increase by 2, and the y-intercept is 125, and that is the starting value. So, y=2x+125 goes with the second choice on the right. For y=1/2x+125 means that 125 is still the starting value but instead of the total amount increasing by 2, it is divided by 2 and goes with the first choice on the right. For y=125x+2, the slope is 125 and 2 is the y-intercept, so the answer is the last one on the right.
