Question

[Bùi Gia Linh]

B=1/1×2+1/2×3+1/3×4+.....+1/2009×1010

Answer 1

[Minh Hồng]

\(B=\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+...+\dfrac{1}{2009\times2010}\\ =\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2009}-\dfrac{1}{2012}\\ =1-\dfrac{1}{2010}=\dfrac{2009}{2010}\)

Answer 2

[phạm quang lộc]

Sửa đề :

\(B=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2009.2010}\)

\(B=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2009}-\dfrac{1}{2010}\)

\(B=\dfrac{1}{1}-\dfrac{1}{2010}\)

\(B=\dfrac{2009}{2010}\)