B and C are absurd; if a series converges, it must have a sum, but if a series diverges, it cannot have a sum.
Now, notice that
![\dfrac12+\dfrac29+\dfrac4{27}+\dfrac8{81}+\cdots=\dfrac12+\dfrac{2^{2-1}}{3^2}+\dfrac{2^{3-1}}{3^3}+\dfrac{2^{4-1}}{3^4}+\cdots](https://tex.z-dn.net/?f=%5Cdfrac12%2B%5Cdfrac29%2B%5Cdfrac4%7B27%7D%2B%5Cdfrac8%7B81%7D%2B%5Ccdots%3D%5Cdfrac12%2B%5Cdfrac%7B2%5E%7B2-1%7D%7D%7B3%5E2%7D%2B%5Cdfrac%7B2%5E%7B3-1%7D%7D%7B3%5E3%7D%2B%5Cdfrac%7B2%5E%7B4-1%7D%7D%7B3%5E4%7D%2B%5Ccdots)
That is, we can write the sum more compactly as
![\dfrac12+\dfrac12\displaystyle\sum_{n=1}^\infty\left(\frac23\right)^n](https://tex.z-dn.net/?f=%5Cdfrac12%2B%5Cdfrac12%5Cdisplaystyle%5Csum_%7Bn%3D1%7D%5E%5Cinfty%5Cleft%28%5Cfrac23%5Cright%29%5En)
The series is geometric with common ratio
![\dfrac23](https://tex.z-dn.net/?f=%5Cdfrac23%3C1)
, so the series converges (and thereby has a sum), so the answer is D.
Answer:
95% confidence interval: (0.325 ,0.383)
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 231
Sample mean = 0.354 ppm
Sample standard deviation = 0.231 ppm
95% confidence interval:
Putting the values, we get,
Answer: Rounded: 236 seconds
Not rounded: 236.07 seconds
Step-by-step explanation: We know that it takes the car 54.9 seconds to travel one mile, and we know that 1 times 4.3 is 4.3, so 4.3 times 54.9 equals 236.07 seconds.
Answer
DescriptionIn mathematics, a zero of a real-, complex-, or generally vector-valued function, is a member of the domain of such that vanishes at; that is, the function attains the value of 0 at, or equivalently, is the solution to the equation. A "zero" of a function is thus an input value that produces an output of.
Step-by-step explanation:x is the connection of the y intercept in a equation dealing with a graph or coordinates.
I think it’s b
Not for sure but it makes the most sense