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>
Answer:
0.2297453
Step-by-step explanation:
Given that :
Total faces of = 12 labeled 1 - 12
Probability of showing a 2 ;
P = required outcome / Total possible outcomes
P(showing a 2) = 1 /12
Hence, probability of not showing a 2 ;
P(showing a 2)' = 1 - 1/2 = 11/12
Probability that atleast one of 3 cubes shows a 2 :
1 - P(none of the cubes shows a 2)
P(none of the cubes shows a 2) =
(11/12 * 11/12 * 11/12) = 0.7702546
1 - 0.7702546 = 0.2297453
Example of non-correlation. Radios and insane people have no logical or mathematical connection whatsoever.
Answer:
5. Mark had 6 laps and John has 42 laps. So you could do a sentence like: John has 42 laps and Mark has 6 laps. What is the diffrence between the two laps?
6. Im not sure about this one :/. Im truly sorry. :(. Good luck tho!
Step-by-step explanation:
Part A: Greg mixed 2 cups of yellow paint with one cup of blue paint to make green paint.
Part B: He needs to add half a cup of blue paint to one cup of yellow paint because there needs to be one cup of blue, for every two cups of yellow.
Part C: The unit price for one cup of yellow paint is $9.