Three interesting infinite series

Numberphile takes a look at three interesting infinite series. The first is 1 + 1/2 + 1/4 + 1/8... which equals 2. The second is 1 + 1/2 + 1/3 + 1/4 + 1/5... which equals infinity. The third is 1 + (1/2)2 + (1/3)2 + (1/4)2... which π2/6