Cho S= 1- 1/2 + 1/3 – 1/4 +….+ 1/2011 – 1/2012 + 1/2013 P= 1/1007 + 1/1008 +….+ 1/2012 + 1/2013 Tính (S-P)^2013

0 bình luận về “Cho S= 1- 1/2 + 1/3 – 1/4 +….+ 1/2011 – 1/2012 + 1/2013 P= 1/1007 + 1/1008 +….+ 1/2012 + 1/2013 Tính (S-P)^2013”

1. Đáp án:

   Ta có :

   `S = 1- 1/2 + 1/3 – 1/4 +….+ 1/2011 – 1/2012 + 1/2013`

   `S = (1+1/3+1/5+…+1/2013)-(1/2+1/4+1/6+…+1/2012)`

   `S = (1+1/2+1/3+1/4+1/5+…+1/2013)-2(1/2+1/4+…+1/2012)`

   `S = (1+1/2+1/3+1/4+1/5+…+1/2013)-(1+1/2+…+1/1006)`

   `S = 1/1007+1/1008+1/1009+…+1/2013 = P`

   `->` S – P = (1/1007+1/1008+1/1009+…+1/2013)-(1/1007+1/1008+1/1009+…+1/2013) = 0`

   `-> (S-P)^2013 = 0^2013=0`

   `Go od luck!`

   Có thắc mắc thì hỏi 

    

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