Question

Express the function as the sum of a power series by first using partial fractions.

f(x)= 13/(x^2 − 3x − 40)

sum n=0 to infinity

Answer 1

f(8) is undefined..

Answer 2

?

Answer 3

fortunately this problem has been cooked so the partial fractions are easy to find

Answer 4

\[\frac{13}{(x-8)(x+3)}=\frac{A}{x-8}+\frac{B}{x+3}\] you know how to find the partial fractions?

Answer 5

stupid typo
\[\frac{13}{(x-8)(x+5)}=\frac{A}{x-8}+\frac{B}{x+5}\]

Answer 6

you can eyeball them
i can show you a snap way to do it if you like

Answer 7

or did you find them already?

Answer 8

sum n=0 to inifnity [(-5)^n+1 -(1/(8^n+1))]x^n is that correct??:S

Answer 9

i kinda doubt it, maybe

Answer 10

oh maybe it is right lets see

Answer 11

ok.s

Answer 12

\[\frac{1}{x-8}=-\frac{1}{8-x}=-\frac{1}{8}\frac{1}{1-\frac{x}{8}}\]
\[=-\frac{1}{8}(1+\frac{x}{8}+\left(\frac{x}{8}\right)^2+...\]

Answer 13

\[=-\sum(\frac{x}{8})^n\] if my algebra is correct

Answer 14

the next one alternates
\[\sum(-1)^n(\frac{x}{5})^n\]

Answer 15

so your answer looks right except i think you made a typo

Answer 16

typo ..where?