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 April 29th, 2019, 01:32 AM #1 Member   Joined: Feb 2018 From: Iran Posts: 52 Thanks: 3 Fractions How to solve the following question please explain step by step
 April 29th, 2019, 02:55 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,921 Thanks: 2203 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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