# 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 \( \displaystyle \sum_{i=1}^7 \frac1{a_i} \).