Text description - screencast for exercise 2

[The narrator reads out the onscreen text.]

NARRATOR: Exercise 2. Find the limiting sum for the geometric series 3 on 2 plus 9 on 8 plus 27 on 32 plus, etc. In this geometric series, the first term is 3 on 2. So a is equal to 3 on 2. The common ratio, r, can be determined by dividing consecutive terms in the series. 9 on 8 divided by 3 on 2 is equivalent to 9 and 8 multiplied by two-thirds, which is 18 on 24 or three-quarters. Similarly, 27 divided by 32 divided by 9 on 8 is equal to 27 on 32 times eight-ninths, which is also three-quarters.

And so we establish a common ratio, r equals three-quarters. The limiting sum of a geometric series is S infinity which is equal to a divided by 1 minus r. In this case, a is 3 on 2 and r is three-quarters. So the limiting sum is 3 on 2 divided by 1 minus three-quarters, that is 3 on 2 divided by a quarter or 3 on 2 multiplied by 4, which is 12 on 2 or 6. So the limiting sum for the geometric series is 6.