Exercise 2 Page 272

Some people are tempted to solve an exercise like this by completing Pascal's Triangle to the tenth row, then adding the terms. However, this sequence of numbers $1,$ $2,$ $4,\dots$ appears in a lot of different mathematics, so it is worth taking a look at this sequence as it is. Let's first have a look at the ratios between terms. Since these terms do have a common ratio of $2,$ we can find each subsequent term by multiplying the previous one by $2$ (also known as doubling). Let's look at just the last part of the sequence and carry it out two more terms to get to the tenth term.

This means the sum of the terms in the tenth row of Pascal's Triangle is $512.$