Summations and integrals with no upper limits I've seen expressions like:
$$\sum\limits_{i} f(x)$$
And
$$
\int\limits_\mathbb{R}f(x)dx
$$
What does it mean that they have no upper limits?

Let's give an example for summation:
$$
\sum_k \binom{n}{k}(-1)^k \left( 1 - \frac{k}{n} \right)^n
$$
Since $\binom{n}{k}$ is defined as being $0$ except when $0 \leq k \leq n$ this sum is the same as 
$$
\sum_{k=0}^n \binom{n}{k}(-1)^k \left( 1 - \frac{k}{n} \right)^n
$$
and is neater to write.
By the way, as a softball follow-on question, show that the sum we are talking about is $$\frac{n!}{n^n}$$
As to integrals over $\Bbb{R}$ that just means an integral from $-\infty$ to $+\infty$. But I am disturbed by not seeing the $dx$ in the integrand. 
