Question 232822
three resistors with values of 1000 ohms, 2200 ohms and 3900 ohms are wired in parallel.To find the total resistance one must add the reciprocals.In the book I am studying the formula to solve is given as:
1/R = 1/R1 + 1/R2 + 1/R3 = 1/1K + 1/2.2K + 1/3.9K = 1/584.5, therefore R = 584.5 ohms 
Can you show me how this answer is computed in long hand? 
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It's as you did it.  You can do 2 resistors 1st, then add the 3rd as a check.
There's a shortcut that works easily with 2 resistors, sum/product
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The 1K and 2.2K --> 1*2.2/(1+2.2)
= 2.2/3.2 = 11/16 K 
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Then:
(11/16)*3.9/(11/16 + 3.9) = 2.68125/4.5875
= 0.58446... K
= 584 ohms