Theorem: 1 = 1/2 [For "Series"ous Minded Students]
Proof:
Start with the infinite series 1/(1*3) + 1/(3*5) + 1/(5*7) + 1/(7*9) + ...
Rewrite it as 1/2[(1/1  1/3) + (1/3  1/5) + (1/5  1/7) + (1/7  1/9) + ... ]
Go back and check that the above series are the same!
Since all terms after 1/1 cancel, the sum of the series is 1/2.
Now, we can also rewrite the original series as (1/1  2/3) + (2/3  3/5) + (3/5  4/7)
+ (4/7  5/9) + ...
Again, all terms after 1/1 cancel, so that the sum is 1.
Thus 1/2 = 1.
What's wrong?
