Theorem: 1 = 1/2:Proof:We can re-write 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 re-write 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. |
