Answer:
Step-by-step explanation:
Check attachment for solution.
Let assume n = k, it does not change anything
Given the series
Σ(-1)ⁿ / (2n+1)ⁿ from n=1 to n= infinity
We can express the series as the sum of partial sums and infinite remainder
S = Sn + Rn
The partial sum is already set to the 3rd terms since the upper bound is given to be 3
So, the error should be from the 4th term to infinity.
NOTE: the error is dominated by the first term of the error. The first term of the error is the fourth term.
Therefore,
The error bound = the value of the fourth term
So, when n = 4
Rn = (-1)ⁿ / (2n + 1)³
R4 = (-1)⁴ / (2•4 + 1)³
R4 = 1 / (8 + 1)³
R4 = 1 / 9³
Rn = 1 / 729
The error bound is positive
Answer:
0.089557
Step-by-step explanation:
Given thqt:
Mean, m = 45000
Standard = 10000
What percentage of trucks can be expected to travel either below 30 or above 65 thousand miles in a year
Below 30, 000
P(x < 30000)
Obtain the standardized score :
Z = (x - m) / s
Z = (30000 - 45000) / 10000
Z = - 15000 / 10000
Z = - 1.5
P(Z < - 1.5) = 0.066807
Above 65,000
P(x > 65000)
Obtain the standardized score :
Z = (x - m) / s
Z = (65000 - 45000) / 10000
Z = 20000 / 10000
Z = 2
P(Z > 2) = 0.02275 (Z probability calculator)
P(Z < - 1.5) + P(Z > 2)
0.066807 + 0.02275
= 0.089557
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