Help with B and C please
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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Help with B and C please
![Let \( S = \sum_{n=1}^{\infty} a_n \) be an infinite series such that \( S_N = 4 - \frac{7}{N^2} \).
**(a)** What are the values of \( \sum_{n=1}^{10} a_n \) and \( \sum_{n=4}^{16} a_n \)?
\[
\sum_{n=1}^{10} a_n = 3.93
\]
\[
\sum_{n=4}^{16} a_n = 0.75043
\]
**(b)** What is the value of \( a_3 \)?
\[
a_3 = \frac{7}{5}
\]
**(c)** Find a general formula for \( a_n \).
\[
a_n = -\frac{7(2n-1)}{(n^2(n-1)^2)}
\]
**(d)** Find the sum \( \sum_{n=1}^{\infty} a_n \).
\[
\sum_{n=1}^{\infty} a_n = 4
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Transcribed Image Text:Let \( S = \sum_{n=1}^{\infty} a_n \) be an infinite series such that \( S_N = 4 - \frac{7}{N^2} \).
**(a)** What are the values of \( \sum_{n=1}^{10} a_n \) and \( \sum_{n=4}^{16} a_n \)?
\[
\sum_{n=1}^{10} a_n = 3.93
\]
\[
\sum_{n=4}^{16} a_n = 0.75043
\]
**(b)** What is the value of \( a_3 \)?
\[
a_3 = \frac{7}{5}
\]
**(c)** Find a general formula for \( a_n \).
\[
a_n = -\frac{7(2n-1)}{(n^2(n-1)^2)}
\]
**(d)** Find the sum \( \sum_{n=1}^{\infty} a_n \).
\[
\sum_{n=1}^{\infty} a_n = 4
\]
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