I don't like this cover particularly much, but it definitely stays true to the feel of the original.
"Bye bye love" is a pretty funny one by S&G as the lyrics are all about heartache bordering full on depression, but people love to clap along to the upbeat melody.
I didn't see the pattern either and had to look it up. Apparently, you can rewrite 1 + 1/(1+2) + 1/(1+2+3)+... as 2(1 - 1/2 + 1/2 - 1/3 +...+1/n - 1/(n + 1)) = 2(1 - 1/(n + 1))
From there, the limit of 2 is obvious, but I guess you just have to build up intuition with infinite sums to see the reformulation.