Question

Làm giúp mình bài 6 cầu xin các bạn 🙏🏻🙏🏻🙏🏻

Answer 1

\(a,\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{20.21}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{20}-\dfrac{1}{21}\)

\(=1-\dfrac{1}{21}=\dfrac{20}{21}\)

Answer 2

\(b,\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{9.11}\)

\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{11}\)

\(=1-\dfrac{1}{11}=\dfrac{10}{11}\)

Answer 3

\(c,\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{9.11}\)

Đặt \(\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{9.11}=A\)

\(2A=\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{9.11}\)

\(2A=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{11}\)

\(2A=1-\dfrac{1}{11}=\dfrac{10}{11}\)

\(A=\dfrac{10}{11}:2=\dfrac{5}{11}\)