The error is actually of the form , where depends on the second derivative of f. Let's assume it is exactly , with unknown , and call the unknown integral I. Then you have the equationsOriginally Posted bymsm1593

Thus your can solve for I: with an error of the order , thus correct to two or three decimal digits.

This is called "Aitken extrapolation" and in this context as "Romberg integration", so you should give proper attribution.

No it isn't2) this problem i don't really have any idea what to do whatsoever, and it's a proof (which are gods way of punishing those you take math classes)

i need to integrate R(x) = t^(x-1)e^(-t)dt from zero to infinity

then prove that R(x+1) = nRn

i tried working out the anitderivate for the start, and i came out with just (t^(x+1)e^(-t)) / ln(t)

i'm not really even sure if that is correct

Try integration by parts in the improper integral. This is known as the Gamma function,

and the formula is the functional equation of the Gamma function.