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infinite series of unit fractions which add to 1

1/2 + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6) + ...
= (2-1)/2 + (3-2)/(2*3) + (4-3)/(3*4) + (5-4)/(4*5) + (6-5)/(5*6) + ...
= (1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) + ...
= 1 + (-1/2 + 1/2) + (-1/3 + 1/3) + (-1/4 + 1/4) + (-1/5 + 1/5) + (-1/6 + ...
= 1 + 0 + 0 + 0 + ) + ...
= 1

Kermit Rose
kermit@polaris.net

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