Question

Tính tổng :

\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{2010\cdot2011}\)

Answer 1

Đặt :

\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...........+\dfrac{1}{2010.2011}\)

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...........+\dfrac{1}{2010}-\dfrac{1}{2011}\)

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

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

~ Chúc bn học tốt ~

Answer 2

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{2010.2011}\)

\(=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2010}-\dfrac{1}{2011}\)

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

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

Answer 3

gọi biểu thức là A

\(A=1.\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+.....+\dfrac{1}{2010}-\dfrac{1}{2011}\right)\)

\(A=1.\left(1-\dfrac{1}{2011}\right)=\dfrac{2010}{2011}\)

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