Therth term of a series (forr=1, 2, ...) is . Prove that the sumSof the firstnterms of the series is given by

Show that

Hence prove that the error in the approximate formula

I have foundScorrectly, my proof of the second part is not quite satisfactory to me, and I don't know how to do the last part.

Proof:

For allr, is positive, hence is positive.

When , , hence

For allr,

Hence, .

For this last part, I did find the general term, but don't know how to find the sum of the series.

Thanks!