The rth term of a series (for r=1, 2, ...) is . Prove that the sum S of the first n terms of the series is given by
Hence prove that the error in the approximate formula
I have found S correctly, my proof of the second part is not quite satisfactory to me, and I don't know how to do the last part.
For all r, is positive, hence is positive.
When , , hence
For all r,
For this last part, I did find the general term, but don't know how to find the sum of the series.