Answer:
a) -7/9
b) 16 / (n² + 15n + 56)
c) 1
Step-by-step explanation:
When n = 1, there is only one term in the series, so a₁ = s₁.
a₁ = (1 − 8) / (1 + 8)
a₁ = -7/9
The sum of the first n terms is equal to the sum of the first n−1 terms plus the nth term.
sₙ = sₙ₋₁ + aₙ
(n − 8) / (n + 8) = (n − 1 − 8) / (n − 1 + 8) + aₙ
(n − 8) / (n + 8) = (n − 9) / (n + 7) + aₙ
aₙ = (n − 8) / (n + 8) − (n − 9) / (n + 7)
If you wish, you can simplify by finding the common denominator.
aₙ = [(n − 8) (n + 7) − (n − 9) (n + 8)] / [(n + 8) (n + 7)]
aₙ = [n² − n − 56 − (n² − n − 72)] / (n² + 15n + 56)
aₙ = 16 / (n² + 15n + 56)
The infinite sum is:
∑₁°° aₙ = lim(n→∞) sₙ
∑₁°° aₙ = lim(n→∞) (n − 8) / (n + 8)
∑₁°° aₙ = 1
Answer:
<h2>37/9</h2>
Step-by-step explanation:
<h3>we have</h3>
<h3>3.77777... :- is a repeating decimal</h3>
<h3>Let</h3>
<h3>x = 3.7...</h3>
<h3>so</h3>
<h3>10x =37.7...</h3>
<h3>10x - x = 37.7... -3.7...</h3>
<h3>9x=34</h3>
<h3>x= 34/9</h3>
<h3>convert to mixed number</h3>
<h3>34/9=(27/9)+(7/9)=3+(7/9) =37/9</h3>
<h3> I hope this may help you.</h3>
The answer is given below:
Answer: To find the third side of a triangle (there are two answers you could get), you need to use the Pythagorean formula: a^2+b^2=c^2. First answer, 3^2+5^2=c^2. Solve for c. c=5.83. The second answer, 3^2+b^2=5^2. Solve for b. b=4.
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<h2>
Automobile must travel at 96 mph to pass the truck in 4 seconds.</h2>
Step-by-step explanation:
Length of automobile = 16 feet = 4.88 m
Length of truck = 28 feet = 8.53 m
Speed of truck = 30 mph = 48 km/h = 13.33 m/s
Time in which automobile to pass truck = 4 s
Distance traveled by truck in 4 seconds = 4 x 13.33 = 53.33 m
Distance which need to cover by automobile in 4 seconds to pass truck is the sum of length of automobile, length of truck and distance traveled by truck in 4 seconds.
Distance which need to cover by automobile in 4 seconds = 4.88 + 8.53 + 53.33
Distance which need to cover by automobile in 4 seconds = 66.74 m
Distance = Speed x Time
66.74 = Speed x 4
Speed = 16.69 m/s = 60 km/h = 96 mph
Automobile must travel at 96 mph to pass the truck in 4 seconds.
