Computing Large Integers with Precision: Solving Equations with x=10^30

[saubbie]

Homework Statement

I need to find some huge numbers and don't know how to do it using a computer. Everything that I have tried doesn't work because the numbers are too big.

Homework Equations

The equations are 1/((1-x)(1-x^2)(1-x^3)) and 1/((1-x)(1-x^3)(1-x^4)) where x=10^30.

The Attempt at a Solution

I am assuming the only way to find this is using a computer. Please help!

 

[Gib Z]

The numbers aren't huge here, they're extremely small!

x is quite a large number here, in comparison the 1's in the denominators will be quite insignificant. If we forget about the 1's, we can the equations to be:

$$\frac{-1}{x^6}$$ and $$\frac{-1}{x^8}$$. Those numbers you can easily compute exactly by hand =] I also assure you that neglecting the 1's creates a very small error indeed. We could carry out an analysis to find the maximum error made, but I can't be bothered, I'm sure you see its tiny as well.