Confusing sum of fractionsQuestion is to find the sum of: ( 1 2 2 − 1 ) + ( 1 4 2 − 1 ) + ( 1 6 2 − 1 ) + ( 1 20 2 − 1 )I know that a 2 − b 2 = ( a + b ) ( a − b ) , and that with this I can find the LCM to be 1995, but this isn't helping me find the answer. I am looking for some kind of formula, because this question can come in an exam (having 60 qs for 60 mins), so they must not be giving a brute-force approach question.Please help me in finding a fast approach.Thanks

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Confusing sum of fractionsQuestion is to find the sum of:  (      1                  2        2            −      1        )  +  (      1                  4        2            −      1        )  +  (      1                  6        2            −      1        )  +  (      1                  20        2            −      1        )I know that       a    2    −      b    2    =  (  a  +  b  )  (  a  −  b  ) , and that with this I can find the LCM to be 1995, but this isn&#039;t helping me find the answer. I am looking for some kind of formula, because this question can come in an exam (having 60 qs for 60 mins), so they must not be giving a brute-force approach question.Please help me in finding a fast approach.Thanks

Carmelo Payne · Accepted Answer

It&#039;s also true that      1          (      a      +      b      )      (      a      −      b      )        =      1          2      b            (          1              a        −        b              −          1              a        +        b              )  Thus you can write your sum as (choosing   b  =  1 in every term)      1    2        (          1      1        −          1      3        +          1      3        −          1      5        +          1      5        −          1      7        +          1      19        −          1      21        )

Confusing sum of fractionsQuestion is to find the sum of: ( 1 2 2 −...

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