I know a series such as:
$$\sum_{i=1}^{n} 3i+1 \quad n\in\mathbb{N}$$
Is Arithmetic and has a difference value of $3$.
I also know a series such as:
$$\sum_{i=1}^{n} {1\over{2^i}} \quad n\in\mathbb{N}$$
Is Geometric and has a common ratio of $1\over 2$.
But what about a series like this? $$\sum_{i=1}^{n} {i\over{2^i}} \quad n\in\mathbb{N}$$
Is there any name for such type of series? If so, does it follow any type of pattern/law such as the difference value and the common ratio?