Step-by-step explanation:
A Maclaurin series is a Taylor series that's centered at 0.
f(x) = ∑ₙ₌₀°° f⁽ⁿ⁾(0) / n! xⁿ
If we substitute f⁽ⁿ⁾(0) = (n + 1)!:
f(x) = ∑ₙ₌₀°° (n + 1)! / n! xⁿ
f(x) = ∑ₙ₌₀°° (n + 1) xⁿ
Use ratio test to find the radius of convergence.
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(n + 2) xⁿ⁺¹] / [(n + 1) xⁿ]│< 1
lim(n→∞)│(n + 2) x / (n + 1)│< 1
│x│< 1
R = 1
I believe the perimeter is 232. Since it's a regular polygon that means all the sides are equal so you take the two expressions on the sides of the polygon and set them equal to each other. Now you know that x=22 so you take that value and substitute it into one of the expressions to get the side length (x+7➡️22+7=29) now we know that each side length is 29. Since there are 8 sides you multiply 29 by 8 and get 232. Hope this helped!
Answer:
Step-by-step explanation:
Let be a random variable that counts the number of failures preceding the first success and be a random variable that counts the number of failures between the first two successes. The probability of success in a independent trial is and both of them have Bernoulli distribution.
Assume that the number of unsuccessful trials before the first successful one is and that is a number of failures between two successes.
The joint mass function of two discrete random variables and is defined by
In this case, we have two discrete random variables and which are independent, so we have that their joint mass function is of the form
The probability that the number of failures before the first successful trial is equal to is
The probability that the number of failures between two successes is equal to is
Therefore,
Now, we obtain that that their joint mass function is
34cm
52/13=4, the smallest side
then 13+4+13+4= 34cm