I alway prefer this type of approach for solving problems. Even when formal proofs are required, I usually get the answer in this way and then reverse engineer

I alway prefer this type of approach for solving problems. Even when formal proofs are required, I usually get the answer in this way and then reverse engineer the proof. Another example (the sum of 1/2 + 1/4 + 1/8 + 1/16...): http://media-2.web.britannica.com/eb-media/79/26979-004-CF3F4DA2.gif http://media-2.web.britannica.com/eb-media/79/26979-004-CF3F...