Find a general formula for $c_{n+1}=c_n+\frac1{c_n}$ (Recursive)

Question

Find a general formula for $c_{n+1}$

If $c_1 = 1$ and $$c_{n+1} = c_n + \frac{1}{c_n}$$

$$c_1 = 1$$

$$c_2 = 1 + 1 = \frac{2}{1}$$

$$c_3 = 2 + 1/2 = \frac{5}{2}$$

$$c_4 = \frac{5}{2} + \frac{2}{5} = \frac{29}{10}$$

$$c_5 = \frac{29}{10} + \frac{10}{29} = \frac{941}{290}$$

score 1 · Accepted Answer · answered Mar 17 '15 at 18:50

1

answered Mar 17 '15 at 18:50

Greg Martin

It doesnt show an explicit formula though? (+1) – Amad27 Mar 17 '15 at 18:54
True, but this does tell you that an explicit formula is probably not known to anyone. – Greg Martin Mar 18 '15 at 00:34

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