Proving the Equality of Simpson's Rule using Trapezoid Rule Approximations

[KingKendrick]

Homework Statement

Integral of f(x)dx from a to b~ S(n) = f(x0) + 4(x1) +2(x2) + 4(x3) + ... 2(xn-2) + 4(xn-1) + f(xn))(Δx/3)

You can use the formula for Simpson's Rule given above, but here is a better way. If you already have the Trapezoid Rule approximations T(2n) and T(n), the next Simpson's rule approximation follows immediately with a simple calculation

S(2n) = (4T(2n) -T(n))/(3)

Verify that for n=8, the two forms of the Simpson's Rule are the same.

Homework Equations

The Attempt at a Solution

I tried to substitute a random function and attempt to go on from there but our professor said that we needed to solve this algebraically. Any help would be appreciated. Thanks!

 

[LCKurtz]

You have to show effort. What did you get for S(16) and (4T(16)-T(8))/3?

Also you left out a bunch of f's in your formula for Simpson's rule.