Answer:
b
Step-by-step explanation:
took the test
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>
<h2><u><em>
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Chickens have 2 legs and cows have 4 legs.
Let x = # of chickens and let y = # of cows.
2x + 4y = 118
x + y = 50
x= 50 - y
2(50 - y) + 4y =118
100 - 2y + 4y = 118
2y = 18
y = 9
x = 41
Answer:
25/2985984
Step-by-step explanation:
12^4*30^8*125^2/(128^4*625^3*27^6)
(2^2*3)^4*(2*3*5)^8*(5^3)^2/(2^7)^4*(5^4)^3*(3^3)^6)
(2^8*3^4*2^8*3^8*5^8*5^6)/(2^28*5^12*3^18)
2^(8+8-28)*3^(4+8-18)*5^(8+6-12)
2^-12*3^-6*5^2
25/(2^12*3^6)
25/2985984
