# 11.5.2. Series and Summation Notation

After a gold mine was discovered, its production in the first year was kg, and the production after that every year was decreasing by of that of the year before. Use the summation notation to determine the amount of the produced gold during the first five years, and then find this amount and approximate the result to the nearest two decimal places.

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### Example

After a gold mine was discovered, its production in the first year was kg, and the production after that every year was decreasing by of that of the year before. Use the summation notation to determine the amount of the produced gold during the first five years, and then find this amount and approximate the result to the nearest two decimal places.

### Solution

From the given information, the production of the gold mine in the year, , is decreasing year-on-year at a rate of . Hence, . The first 3 years are given by:

Therefore, we can see that the production in the will be given by

Hence, the total production over the first five years is given by the following series:

Applying the formula for geometric series gives us

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