Discrete Mathematics with Graph Theory

by Goodaire and Parmenter

Page 182 # 10b

a_{n}= -10a_{n-1}- 25a_{n-2}, n ≥ 2, given a_{0}=1, a_{1}= 25

So far I have:

f(x) - a_{0}-a_{1}x = -10x(f(x) - a_{0}) - 25x^{2}f(x)

f(x) - 1 -25x = -10x(f(x) - 1) - 25x^{2}f(x)

Then solving for f(x)

I get:

f(x) = (1+35x)/(1+10X+25x^{2})

f(x) = (1+35x)/(1+5x)^{2}

Then when I do partial fractions I get:

(1+35x) = (A/(5x+1)^2) + (B/(5x+1))

Then solving for A & B I get:

A = 7

B = -6

And now I'm having trouble finding my acoefficient._{n}