Why does series of a constant diverges?

Question

It is known that the series $\sum_{n=1}^{\infty}3$ diverges, and I suppose it is because the sum of infinitely large amount of terms tends to infinity. But maybe there is some practical proof or theorem about it?

Answer 1

It diverges because:

1. $(\forall N\in\mathbb N):\sum_{n=1}^N3=3N$;
2. $\displaystyle\lim_{N\to\infty}3N=\infty$.

Answer 2

1-Not every constant series diverges. Take $ \sum_1^{\infty} 0=0$

2-However if it is a non-zero constant, say, without loss of generality $\epsilon >0$ then $ \sum_1^{\infty} \epsilon \geq \sum_1^{ n \times\lceil{\frac{1}{\epsilon}}\rceil} \epsilon>n$