Example 2. This is the sum of the first n items of the series formed by the sum of the corresponding items of a arithmetic progression and a geometric progression.

Example 3. Find the sum of the first n terms of the sequence {n× 1/2 n}

This is the sum of the first n items of a series formed by the product of the corresponding items of a arithmetic progression and a geometric progression.

It can be solved by multiplying the common ratio of geometric series by 1/2 and then finding the difference.