Series Exercises

Answer

1. This problem directly tells us everything we need to know. We're given a = 3 and r = 0.2. Since we're asked to find S₇ we use n = 7.

2. We're adding terms with denominators from 7⁰ to 7¹². This means we're adding 13 terms together, so we must be finding S₁₃. The first term is a = 2 and the ratio is .

3. If we expand this series we get

The first term is a = 1, the ratio is , and we're adding n = 10 terms (since the exponents on  go from 0 to 9). Using the formula, we get

4. The first term is  and the ratio is . If we rewrite the denominators, we can see that we're adding 8 terms, so n = 8:

We get

5. If we expand the sum we get

2(0.9)⁶ + ... + 2(0.9)³⁰.

The first term is a = 2(0.9)⁶ and the ratio is r = 0.9. We're adding up terms with exponents from 6 to 30, so we're missing the exponents from 1 to 5.

This means we have

n = 30 – 5 = 25

terms. Applying the formula,

Answer

This expression is not in closed form. As n gets bigger, we have to do more work.

Answer

This expression is in closed form. It doesn't matter how big n gets. We always do the same amount of work.

Answer

This expression is not in closed form. As n gets bigger, we have to do more work.