<p>The past decade has witnessed a growing interest in the truncated theta series, the most interesting of which are the truncated theorems of the three classical theta identities attributed to Euler and Gauss. In this paper, we first classify these truncated series into two types, and then reveal the relationship between them, and finally make a strong conjecture on the truncated Jacobi triple product series, which improves the original conjecture of Andrews and Merca.</p>