We have the recurrence relation:$5x_{n+1}-x_n=\frac{1}{3}$$x_0=\frac{1}{12}$solution:    $y_h=(\frac{1}{5})^nC$   $y_p:  5A-A=\frac{1}{3}  $$ A=\frac{1}{12}$$y=(\frac{1}{5})^nC+\frac{1}{12}$$y(0)=C=0$Will the answer go to $ \frac{1}{12}$ or somewhere very close to $\frac{1}{12}$?The answer sheet says very close to. I thought it would be to exactly $\frac{1}{12}$ because for large n the computer would read the fraction as 0 even though it is not? And how is this not right? Please also explain why the fact that for large power n on fractions like here the fact that the number would be read as 0 would not alter this as that was my reasoning.
problem about simulating recurrence relation
error estimation