What is the sum of the geometric series below? 3+1+1/3+1/9+1/27 a. 67/27 b. 121/27 c. 40/9 d. 41/9
Mathematics · High School · Mon Jan 18 2021
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Given the sequence:
3 + 1 + ⅓ + 1/9 + 1 / 27
Determine the sum of the whole geometric series.
Solution:
In order to determine the sum of the whole geometric series, we must simply add first the whole fractions, the combine later with whole numbers.
= 3 + 1 + ⅓ + 1/9 + 1 / 27
⅓ can be rewritten as 9/27, while 9 can be represented as 3/27.
= 4 + 9/27 + 3/27 + 1 / 27
=4 + 13/27
= 108/27 + 13/27
= 121 / 7
Final answer:
b. 121/27