Continued Fractions: General Statement & Evidence

[Pirate21]

Please help with the following question:

http://img161.imageshack.us/img161/691/continuousfraction5az5.gif

By considering other values of k, determine a generalized statement for the exact value of any such continued fraction. For which values of k does the generalised statement hold true? How do you know? Provide evidence.

Thanks.

 

[jhicks]

Any attempt at a solution? The trick may be slightly hard to see at first, but it's fairly standard. One method to see the answer might be to cover your hand over everything above the second highest 1 in the formula. What do you see?