# 11.5.2. Series and Summation Notation

A child wants to build a pyramid of identical wooden cubes, where its top consists of one cube, the second row consists of two cubes, and the third row consists of three cubes and so on. Express the number of cubes used in building the pyramid using the summation notation, given that the pyramid consists of 5 rows, and find this number.

• A cubes
• B cubes
• C cubes
• D cubes

### Example

A child wants to build a pyramid of identical wooden cubes, where its top consists of one cube, the second row consists of two cubes, and the third row consists of three cubes and so on. Express the number of cubes used in building the pyramid using the summation notation, given that the pyramid consists of 5 rows, and find this number.

### Solution

Let us consider each row of the pyramid starting at the top and moving down. The first row has one cube, so we can say . Following this, each subsequent row has one more cube than the preceding row. Hence, . So, the number of cubes in each row can be expressed as

More generally, we can express the number of blocks in the role as . Therefore, using summation notation, we can express the series for the total number of cubes used building a five-row pyramid, as follows:

Evaluating this series gives the total number of cubes used by the child to create a pyramid of five rows.

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