(2) questions on convergent and divergent

  • #1
1. A year after the leak began the chemical had spread 1500 meters from its source. After two years, the chemical had spread 900 meters more, and by the end of the third year, it had reached an additional 540 meters.
a. If this pattern continues, how far will the spill have spread from its source after 10 years?
b. Will the spill ever reach the grounds of a school located 4000 meters away from the source explain? Explain.

2. None

3. I tried but i can't seem to find the pattern for this problem.
1500, 2400, 2940...

2nd question​

1. Use the comparison test to determine whether each series is convergent or divergent.
1/2 + 1/9 + 1/28 + 1/65 + ...

2. None

3. I tried to solve this problem but I can't seem to find the pattern for it Can you guys show me? Thank You!.
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  • #2
Instead of the total distance, try to first see a connection in the additional distance reached every year.
1500, 900, 540, ...

You will find this is a particular kind of series, and the total distance it has spread from the source in year n is the sum of the first n terms of this series.

For the second one, all you need is something to compare it to. Maybe it helps to note that, 9 <= 9, 16 < 28, 25 < 65, etc.

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