Question

Tính:

\(\dfrac{1}{25.27}+\dfrac{1}{27.29}+\dfrac{1}{29.31}+...+\dfrac{1}{73.75}\)

Answer 1

Gọi \(\dfrac{1}{25.27}+\dfrac{1}{27.29}+\dfrac{1}{29.31}+...+\dfrac{1}{73.75}\)

là A, ta có

\(A=\dfrac{1}{25.27}+\dfrac{1}{27.29}+\dfrac{1}{29.31}+...+\dfrac{1}{73.75}\)

\(\Rightarrow2.A=\dfrac{2}{25.27}+\dfrac{2}{27.29}+\dfrac{2}{29.31}+...+\dfrac{2}{73.75}\)\(\Rightarrow2.A=\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}-\dfrac{1}{29}+...+\dfrac{1}{73}-\dfrac{1}{75}\)\(\Rightarrow2.A=\dfrac{1}{25}-\dfrac{1}{75}\)

\(\Rightarrow2.A=\dfrac{2}{75}\)

\(\Rightarrow A=\dfrac{2}{75}\div2\)

\(\Rightarrow A=\dfrac{1}{75}\)

KL: Vậy A =\(\dfrac{1}{75}\)