Question

[linh]

Answer 1

[HT.Phong (9A5)]

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

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

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

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

b) \(B=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{2009.2011}\)

\(B=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2009}-\dfrac{1}{2011}\)

\(B=1-\dfrac{1}{2011}\)

\(B=\dfrac{2010}{2011}\)

Answer 2

[Lê Duy Minh Quang]

b) B= \(\dfrac{2}{1.3}\)+ \(\dfrac{2}{3.5}\)+ ... + \(\dfrac{2}{2010.2012}\)

B= 1 - \(\dfrac{1}{3}\)+ \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\)+...+ \(\dfrac{1}{2010}\) - \(\dfrac{1}{2012}\)

B= 1 - \(\dfrac{1}{2012}\)

B= \(\dfrac{2011}{2012}\)