1. The problem statement, all variables and given/known data
This is problem 1.14.8 in Mary Boas: Math for Phys. Sci.
Estimate the error if [tex] f(x)=\sum _{ n=1 }^{ \infty }{ \frac { { x }^{ n } }{ { n }^{ 3 } } } [/tex] is approximated by the sum of its first three terms
for |x| < 1/2 .
2. Relevant equations
[tex]Error\quad <\quad \left| \frac { { a }_{ N+1 }{ x }^{ N+1 } }{ 1-\left| x \right| } \right| [/tex]
3. The attempt at a solution
I got the solution manual answer using x=1/2 (Error < 0.002), but shouldn't x=-1/2 be the same error using the equation above? I must be missing something. The manual gives the error .001 for x<0.
This is problem 1.14.8 in Mary Boas: Math for Phys. Sci.
Estimate the error if [tex] f(x)=\sum _{ n=1 }^{ \infty }{ \frac { { x }^{ n } }{ { n }^{ 3 } } } [/tex] is approximated by the sum of its first three terms
for |x| < 1/2 .
2. Relevant equations
[tex]Error\quad <\quad \left| \frac { { a }_{ N+1 }{ x }^{ N+1 } }{ 1-\left| x \right| } \right| [/tex]
3. The attempt at a solution
I got the solution manual answer using x=1/2 (Error < 0.002), but shouldn't x=-1/2 be the same error using the equation above? I must be missing something. The manual gives the error .001 for x<0.
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