Question

[Dương Hạ Chi]

Lm hộ mk bài 2 nha!

Answer 1

[Nguyễn Thanh Hằng]

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 :

\(B=\dfrac{1}{1.6}+\dfrac{1}{6.11}+.......+\dfrac{1}{496.501}\)

\(5B=\dfrac{5}{1.6}+\dfrac{5}{6.11}+............+\dfrac{5}{496.501}\)

\(5B=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...........+\dfrac{1}{496}-\dfrac{1}{501}\)

\(5B=1-\dfrac{1}{501}\)

\(5B=\dfrac{500}{501}\)

\(\Rightarrow B=\dfrac{500}{501}:5=\dfrac{100}{501}\)

~ Học tốt ~