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Answer:
1/2 + 1/6
Step-by-step explanation:
2/3 = 1/2 + 1/6
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The sum of unit fractions is called an Egyptian Fraction. There are several different algorithms for finding such a sum. Here, we are starting with the form ...
2/p
where p is a small prime. Then the sum can be written as ...
1/((p+1)/2) +1/(p(p+1)/2) = 1/(4/2) +1/(3(4/2)) = 1/2 + 1/6
A different algorithm is used when p is a composite number.
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Using the "greedy" algorithm, we can find the largest unit fraction less than 2/3 to be ...
1/ceil(3/2) = 1/2
Then the largest unit fraction in the remainder is similarly found. The remainder is ...
2/3 -1/2 = 1/6 . . . . already a unit fraction
So, the sum is ...
2/3 = 1/2 + 1/6
