Bài 2 :
a)Ta có :
\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+.............+\dfrac{1}{999.1000}\)
\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+.............+\dfrac{1}{999.1000}\)
\(A=1-\dfrac{1}{1000}\)
\(A=\dfrac{999}{1000}\)
b) Ta có :
\(B=\dfrac{1}{1.6}+\dfrac{1}{6.11}+.......+\dfrac{1}{496.501}\)
\(5B=\dfrac{5}{1.6}+\dfrac{5}{6.11}+............+\dfrac{5}{496.501}\)
\(5B=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...........+\dfrac{1}{496}-\dfrac{1}{501}\)
\(5B=1-\dfrac{1}{501}\)
\(5B=\dfrac{500}{501}\)
\(\Rightarrow B=\dfrac{500}{501}:5=\dfrac{100}{501}\)
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