chứng minh rằng 1-1/12+1/3-1/4+1/5-1/6+…+1/99-1/100=1/51+1/52+..+1/100

0 bình luận về “chứng minh rằng 1-1/12+1/3-1/4+1/5-1/6+…+1/99-1/100=1/51+1/52+..+1/100”

1.     1 – 1/2 + 1/3 – 1/4 + 1/5 – 1/6 + … + 1/99 – 1/100 

   = (1 + 1/3 + 1/5 + … + 1/99) – (1/2 + 1/4 + … + 1/100)

   = (1+1/3+1/5+…+1/99) – (1/2+1/4+…+1/100) + (1/2+1/4+…+1/100) – (1/2+1/4+…+1/100)

   = [(1+1/3+1/5+…+1/99) + (1/2+1/4+…+1/100)] – [(1/2+1/4+…+1/100) – (1/2+1/4+…+1/100)]

   = (1+1/2+1/3+1/4+…+1/100) – (1/2+1/4+…+1/100)×2

   = (1+1/2+1/3+1/4+…+1/100) – (1/1+1/2+…+1/50)

   = 1/51+1/52+..+1/100    (đpcm)

    

   Bình luận