The following alternating series converge to given multiples of π . Find the value of N predicted by the remainder estimate such that the Nth partial sum of the series accurately approximates the left-hand side to within the given error. Find the minimum N for which the error bound holds, and give the desired approximate value in each case. Up to 15 decimals places, π = 3.141592653589793... 310. [T] Plot the series ∑ n = 1 100 cos ( 2 π n x ) n for 0 ≤ x ≤ 1 . Explain why ∑ n = 1 100 cos ( 2 π n x ) n diverges when x = 0. 1. How does the series behave for other x ?
The following alternating series converge to given multiples of π . Find the value of N predicted by the remainder estimate such that the Nth partial sum of the series accurately approximates the left-hand side to within the given error. Find the minimum N for which the error bound holds, and give the desired approximate value in each case. Up to 15 decimals places, π = 3.141592653589793... 310. [T] Plot the series ∑ n = 1 100 cos ( 2 π n x ) n for 0 ≤ x ≤ 1 . Explain why ∑ n = 1 100 cos ( 2 π n x ) n diverges when x = 0. 1. How does the series behave for other x ?
The following alternating series converge to given multiples of
π
. Find the value of N predicted by the remainder estimate such that the Nth partial sum of the series accurately approximates the left-hand side to within the given error. Find the minimum N for which the error bound holds, and give the desired approximate value in
each case. Up to 15 decimals places,
π
=
3.141592653589793...
310. [T] Plot the series
∑
n
=
1
100
cos
(
2
π
n
x
)
n
for
0
≤
x
≤
1
. Explain why
∑
n
=
1
100
cos
(
2
π
n
x
)
n
diverges when x = 0. 1.
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
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