1/1×5 + 1/5×10 + 1/10×15 +…+1/2010×2015

0 bình luận về “1/1×5 + 1/5×10 + 1/10×15 +…+1/2010×2015”

1. Đặt:

   `A = 1/(1.5) + 1/(5.10) + 1/(10.15) + … + 1/(2010.2015)`

   `A = 1/(1.5) + 1/5 . 5 . (1/(5.10) + 1/(10.15) + … + 1/(2010.2015))`

   `A = 1/(1.5) + 1/5 . (5/(5.10) + 5/(10.15) + … + 5/(2010. 2015))`

   `A = 1/5 + 1/5 . (1/5 – 1/10 + 1/10 – 1/15 + … + 1/2010 – 1/2015)`

   `A = 1/5 + 1/5 . (1/5 – 1/2015)`

   `A = 1/5 . (1 + 1/5 – 1/2015)`

   `A = 1/5 . 2417/2015`

   `A = 2417/ 10075`

   Bình luận

2. Đáp án:

   `1/(1xx5)+\underbrace{1/(5xx10)+1/(10xx15)+….+1/(2010xx2015)}_{B}`

   Ta có:

   `5B=5/(5xx10)+5/(10xx15)+….+5/(2010xx2015)`

   `=>5B=1/5-1/10+1/10-1/15+….+1/2010-1/2015`

   `=>5B=1/5-1/2015`

   `=>5B=402/2015`

   `=>B=402/10075`

   `=>1/5+B=2417/10075`

   Bình luận