`A=1/(1×2)+1/(2×3)+…+1/(99×100)`

2 bình luận về “`A=1/(1×2)+1/(2×3)+…+1/(99×100)`”

1. A = 1/(1 xx 2) + 1/(2 xx 3) + … + 1/(99 xx 100)

   = ((2 – 1))/((1xx2)) + (3-2)/((2xx3)) + … + ((100 – 99))/((99×100))

   = ( 2/(1 xx 2) – 1/(1 xx 2) ) + ( 3/(2 xx 3) – 2/(2xx3) ) + … +  100/(99 xx 100) – 99/(99 xx 100) )

   =  1 – 1/2 + 1/2 – 1/3 + … + 1/99 – 1/100

   = 1 – 1/100

   = 1/99

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2. Giải đáp:

   A=1/(1×2)+1/(2×3)+…+1/(99×100)

   A= 1 – 1/2 + 1/2 – 1/3 + … + 1/99 – 1/100 

   A= 1-1/100

   A= 100/100 – 1/100

   A= 99/100

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