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"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.

Is this a taylor series expansion question? I don't know where to start.

The next one is:

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

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

again, I don't know exactly where to start. Do I rearrange the formula? Do I calculate the relative error?

Any pointers will be greatly appreciated.

CC