How would I write this as a Summation?

Question

I have a function n that I want to write a summation for.

How would I write this as a sum?

$ (1/n_1)+((1/n_2)*(1/n_1))+((1/n_3)*(1/n_2)*(1/n_1))+ ... $ etc.

Answer 1

$$\sum\limits_{i=1}^k \left( \prod\limits_{j=1}^i \frac{1}{n_j} \right)$$