How one could prove, that q pochhammer symbol $(1,1/n) = \prod\_{k = 1}^{\infty}(1-\frac{1}{n^k}) \geq 1 - \frac{1}{n-1}$



Lower bound of q pochhammer symbol
$$\prod (1-x\_i)=1-x\_1-x\_2(1-x\_1)-x\_3(1-x\_1)(1-x\_2)-\ldots \geqslant 1-\sum x\_i, \forall x\_i\in [0,1],$$
use this for $x\_i=1/n^i$.


