Question

tính nhanh: A=\(\dfrac{4}{3}\)+\(\dfrac{4}{15}\)+\(\dfrac{4}{35}\)+......+\(\dfrac{4}{399}\)

Làm giúp mik vs ạ mik cần gấp

Answer 1

\(A=\dfrac{4}{3}+\dfrac{4}{15}+...+\dfrac{4}{399}\)

\(\Rightarrow A=\dfrac{4}{1.3}+\dfrac{4}{3.5}+...+\dfrac{4}{19.21}\)

\(\Rightarrow A=2\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{19.21}\right)\)

\(\Rightarrow A=2\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{19}-\dfrac{1}{21}\right)\)

\(\Rightarrow A=2\left(1-\dfrac{1}{21}\right)\)

\(\Rightarrow A=\dfrac{2.20}{21}=\dfrac{40}{21}\)