Question 200529
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Just add the fractions like any other fractions.  Find the lowest common denominator, convert each of the three fractions, then add the numerators.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 12 = 3 \times 2 \times 2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 15 = 3 \times 5]


And *[tex \LARGE 5] only has the factor *[tex \LARGE 5]


So, you need two 2s, one 3, and one 5 as factors for your LCD.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  2 \times 2 \times 3 \times 5 = 60]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{R_t}= \left(\frac{1}{12}\right)\left(\frac{5}{5}\right) + \left(\frac{1}{15}\right)\left(\frac{4}{4}\right) + \left(\frac{1}{5}\right)\left(\frac{12}{12}\right) = \frac{5}{60}+\frac{4}{60}+\frac{12}{60} = \frac{21}{60} = \frac{7}{20}]


Therefore


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R_t = \frac{20}{7}]


Just a little less than 3.


By the way, your general formula should be represented thus:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{R_t} = \frac{1}{R_1} +  \frac{1}{R_2} +\ .\,.\,.\ + \frac{1}{R_n}]


indicating an indefinite number of terms.




John
*[tex \LARGE e^{i\pi} + 1 = 0]
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