Finnding the error in approximating an infinite series

[PhyStan7]

Hi, sorry i wasnt quite sure where to post this. I think i know how to do it but have not encountered a question like it and don't have a mark scheme so thought id post it up to see if my thinking is correct.

Homework Statement

(c) By considering the integral of 1/(x^3) between N and infinity, where N is an integer, find the error in approximating the sum of 1/(x^3) from r=1 to infinity by its first 5 terms.

Homework Equations

Sum = (sum to N terms) + (1/2)(A[n]+A[n+1])

Where A[N] is the integral of the function from N to infinity
Where A[N+1] is the integral of the function from N+1 to infinity

The Attempt at a Solution

Ok so i think you know the error will be Sum-sum to 5 terms so bring (sum to N terms) to the other side. This will equal the error.

Integrate 1/(x^3) to get -1/(2(x^2)). Putting in x=5 (A[N]) and x=6 (A[N+1]) equal 1/50 and 1/72. Thus the errror = (1/100)+(1/144) or 244/14400

Is this right? The problem really is i can't get hold of a mark scheme to see the correct method.

Thanks!

 

[vela]

I don't see any mistakes.

I tried summing the first 10,000 terms and just the first 5 terms in Mathematica. The difference came out to be 0.0163949. Your error estimate is 0.0169444.