recursive formula for 1, 1/2, 1/3, 1/4

[bobby]

how do you figure out the recursive formula for a sequence. I cannot figure this one out to save my life. 1, 1/2, 1/3, 1/4.

 

[Larry12]

I came to notice that the denominator increases by 1 in each step.
1 / 1 + 1 = 1 / 2 etc.
but i guess thats not what you are asking for >_>

 

[pka]

Does this work?
\(\displaystyle \L n_1 = 1\,\& \,k > 1,\quad n_k = \left[ {\left( {n_{n - 1} } \right)^{ - 1} + 1} \right]^{ - 1}.\)