Question

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D= \(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{199.201}\)

 

 

Answer 1

\(D=\frac{3}{1.3}+\frac{3}{3.5}+...+\frac{3}{199.201}\)

\(D=\frac{3}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{199.201}\right)\)

\(D=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{199}-\frac{1}{201}\right)\)

\(D=\frac{3}{2}\left(1-\frac{1}{201}\right)\)

\(D=\frac{3}{2}.\frac{200}{201}\)

\(D=\frac{100}{67}\)

Answer 2

#)Giải :

\(D=\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{199.201}\)

\(D=\frac{3}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{199.201}\right)\)

\(D=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{199}-\frac{1}{201}\right)\)

\(D=\frac{3}{2}\left(1-\frac{1}{201}\right)\)

\(D=\frac{3}{2}\times\frac{200}{201}\)

\(D=\frac{100}{67}\)

Answer 3

\(\frac{2}{3}D=\frac{2}{1\times3}+\cdot\cdot\cdot+\frac{2}{199\times201}\)

\(\frac{2}{3}D=1-\frac{1}{3}+\cdot\cdot\cdot+\frac{1}{199}-\frac{1}{201}\)

\(\frac{2}{3}D=1-\frac{1}{201}\)

\(\frac{2}{3}D=\frac{200}{201}\)

\(D=\frac{200}{201}:\frac{2}{3}=\frac{200\times3}{201\times2}=\frac{300}{201}\)

Answer 4

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