\(A=\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{39800}\)
\(=\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+...+\dfrac{1}{199\times200}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{199}-\dfrac{1}{200}\)
\(=1-\dfrac{1}{200}=\dfrac{199}{200}\)
\(A=\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{39800}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{199}-\dfrac{1}{200}\)
\(=\dfrac{199}{200}\)
A=1/2+1/6+...+1/39800
=1/1×2+1/2×3+...+1/199×200=1/1×2+1/2×3+...+1/199×200
=1−1/2+1/2−1/3+...+1/199−1/200=1−1/2+1/2−1/3+...+1/199−1/200
=1−1/200=199/200
