1/3 + 1/ 6 + 1/10 + … + 2/x.(x+1) = 998/1000

1 bình luận về “1/3 + 1/ 6 + 1/10 + … + 2/x.(x+1) = 998/1000”

1. 1/3 + 1/6 + 1/10 + … + (2)/(x(x+1)) = 998/1000

   <=> 2/6 + 2/12 + 2/20 + … + (2)/(x(x+1)) = 998/1000

   <=> (2)/(2.3) + (2)/(3.4) + (2)/(4.5) + … + (2)/(x(x+1)) = 998/1000

   <=> 2((1)/(2.3) + (1)/(3.4) + (1)/(4.5) + … + (1)/(x(x+1)) )=998/1000

   <=> 2( 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + … + 1/x – (1)/(x+1) )=998/1000

   <=> 2 (1/2 – (1)/(x+1) ) =998/1000

   <=> 1/2 – (1)/(x+1) = 499/1000

   <=> (1)/(x+1) = 1/1000

   <=> x + 1 = 1000

   <=> x= 999.

    

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