# Numerical Analysis: Evaluating in a numerically stable fashion

Hi, I need help with the following numerical analysis questions. The textbook I'm using (Intro to Numerical Analysis by Stoer) doesn't have many examples so I'm having a lot of trouble figuring out what exactly I should be doing.

"Evaluating the summation as i goes from 1 to n of a sub i in floating point arithemetic may lead to an arbirarily large error. If however, all summands a sub i are of the same sign, then this relative error is bounded. Derive a crude bound for this error, disregarding terms of higher order."

What I did was to expand the n terms in the form [(a+b)(1+esub1)+c](1+esub2)... and then reduce it using the formula for relative error: [fl(y)-y]/y. But the upper bound is given by 5*10^(-t), so what am i supposed to do next?

Another question is:
"Show how to evaluate the following expression in a numerically stable fashion:"

1/(1+2x) - (1-x)/(1+x)

I combined the above to get 2x^2/[(x+1)(2x+1)]. What am I supposed to do next? Am I supposed to come up with an algorithm for solving it then calculate the relative error? The book doesn't really have any worked examples so I'm hopelessly lost.

Thanks for looking.