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evaluate: 1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ... ad infinitum?
1 Answer
- RLeeLv 58 years agoFavorite Answer
Level 1: 1 = 1
Level 2: 1 + 1/(1 + 1) = 1 + 1/2 = 3/2
Level 3: 1 + 1/(1 + 1/(1 + 1)) = 1 + 2/3 = 5/3
Level 4: 1 + 1/(1 + 1/(1 + 1/(1 + 1))) = 1 + 3/5 = 8/5
Level 5: 1 + 5/8 = 13/8
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If this actually converges (and it looks like it will), it will keep going until 1 + x/y = y/x, which means
1 + A = 1/A (where A = x/y)
A + A^2 = 1 (multiplied everything by A)
A^2 + A - 1 = 0
Use the quadradic equation to figure out the answer!!
