Let 1α + 2α + 3α + …. + nα be denoted by Sα. It is well known that Sα can be expressed as a polynomial in n of degree (α + 1). The expressions for S1, S2, S3 …. can be found in succession by elementary methods, which also give numerous relations such as S3 = 12S2S3 = 7S6 + 5S4. The elegant method which I am about to explain is not original. It is due in essence to the Arabian mathematician Alkarkhi (circa 1000 B.C.).