Alternating Summation of Ones
Here is a pretty common high school problem that shows the weirdness that happen with infinite series.
What is the result of 1−1+1−1+1…? We want to know what the value is so set equal to some unknown, like X and notice that it contains itself.
X=1−1+1−1+1−1…−XX=1−X2X=1→X=1/2