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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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