透過數學運算大師MATHEMATICA所提供的之值，我們一起來探討這個無窮級數之和的公式。當s=2m為正偶數之時，MATHEMATICA告訴我們ζ(2)為n2m的有理數倍。在數學運算大師MATHEMATICA的協助之下，我們將帶領由這些個別的函數值ζ(2m)來拼裝出整個公式的形式圖樣。至於s為正奇數之時，MATHEMATICA卻不作任何的表態。事實上，連最簡單的ζ(3)到目前為止還是沒有一個公式如ζ(2m)者存在。這有待您來繼續努力，無限的機會就擺在你面前，不是嗎? We explore a formula for the sum of the infinite series ζ(s)= according to the values provided by MATHEMATICA. When s=2m is an even positive integer. MATHEMATICA tells us that ζ(2m) is just a rational multiple ofπ2m. From these individual function values, with the help of MATHEMATICA, we will guide you to see the pattern of the whole formula. On the other hand, when s is an odd positive integer, MATHEMATICA tells us nothing. In fact, there is no such formula exists even for the simplest ζ(3). The reason remains unknown, so still a lot of chances are waiting for you.
