Here is a pretty common high school problem that shows the weirdness that happen with infinite series.
WhatĀ isĀ theĀ resultĀ ofĀ 1ā1+1ā1+1ā¦? We want to know what the value is so set equal to some unknown, like X and notice that it contains itself.
āX=1ā1+1ā1+1ā1ā¦āāXāX=1āX2X=1āX=1/2āā