/sci/ - Science & Math

>>15110901
If [math]\displaystyle \sum_{n = 1}^{\infty} a_n < 1[/math] then you have that the geometric series [math]\displaystyle \sum_{k = 0}^{\infty} \left( \sum_{n = 1}^{\infty} a_n \right)^k[/math] is also finite, and it should be larger than [math]\lim_{n \to \infty} (1 + a_1) \ldots (1 + a_n)[/math]