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April 29th, 2019, 01:32 AM   #1
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Fractions


How to solve the following question please explain step by step
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April 29th, 2019, 02:55 AM   #2
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If we call the sum S, and note that it has 35 terms,
S = 1/2 - 2/3 + 3/2 - 4/3 + 5/2 - . . . + 31/2 - 32/3 + 33/2 - 34/3 + 35/2.
By rewriting the above sum with the order of its terms reversed,
S = 35/2 - 34/3 + 33/2 - 32/3 + 31/2 - ... + 5/2 - 4/3 + 3/2 - 2/3 + 1/2.

By addition, 2S = 36/2 - 36/3 + 36/2 - 36/3 + 36/2 - . . . + 36/2 (35 terms),
i.e. 2S = 17(18 - 12) + 18 = 17 × 6 + 18 = 120, so S = 60.
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