Consider the infinite series: 1 1-2 1 1 1 +. 7-27 3-2 5-25 a) Write the given numerical series using summation notation.
Consider the infinite series: 1 1-2 1 1 1 +. 7-27 3-2 5-25 a) Write the given numerical series using summation notation.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the infinite series:
1/1(2)-1/3(2)^3+1/5(2)^5-1/7(2)^7+...
I'm having trouble with parts e.) , f.) , g.)
Transcribed Image Text:Consider the infinite series:
+.
7-27
1-2
3-23
5-25
a) Write the given numerical series using summation notation.
b) Identify the power series and the value x=a at which it was evaluated to obtain the given
(numerical) series. Write the power series in summation notation, in terms of x.
c) Find the radius and interval of convergence for the power series in part b).
d) Use properties of power series to construct the function f(x) represented by the power
series in part c).
e) Evaluate f(a), the function from part d) at the value x=a in part b), to find the exact value of
the given (numerical) series.
f) Identify and use an appropriate theorem to calculate the number of terms N of the series
needed to compute the value f(a) with absolute error < 0.00005
g) Verify your answers from parts e) and f) by calculating f(a) from the function f(x) and the
value a, and by calculating N terms of the numerical series. Write each answer to five
decimal places. Calculate the absolute error and verify that it is < 0.00005
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