# Recurring Recursion

Algebra Level pending

${a_n} = \frac{\displaystyle \prod_{k=1}^{n-1} a_k}{\displaystyle \sum_{k=1}^{n-1} a_k}$

If the sequence $$a_n$$ satisfy the recurrence relations formula as described above with $$a_1 = 1$$. Determine the value of $$\displaystyle \sum_{i=1}^7 \frac1{a_i}$$.

×