Theorem: 1 = 1/2: Proof:
We can rewrite the infinite series 1/(1*3) + 1/(3*5) + 1/(5*7) + 1/(7*9) +...
as 1/2((1/1  1/3) + (1/3  1/5) + (1/5  1/7) + (1/7  1/9) + ... ). All terms after 1/1 cancel, so that the sum is 1/2.
We can also rewrite the series as (1/1  2/3) + (2/3  3/5) + (3/5  4/7) + (4/7  5/9) + ...
All terms after 1/1 cancel, so that the sum is 1.
Thus 1/2 = 1.
