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

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SUMMARY

This discussion focuses on computing large integers with precision, specifically solving equations involving x=10^30. The equations presented are 1/((1-x)(1-x^2)(1-x^3)) and 1/((1-x)(1-x^3)(1-x^4)). Participants concluded that for such large values of x, the contributions of the 1's in the denominators are negligible, simplifying the equations to -1/x^6 and -1/x^8, which can be computed manually with minimal error.

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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!
 
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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:

[tex]\frac{-1}{x^6}[/tex] and [tex]\frac{-1}{x^8}[/tex]. 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.
 

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