Question

1) Tính A = \(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{21.23}\)

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Answer 1

\(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{21.23}\)

\(=5-\frac{5}{3}+\frac{5}{3}-\frac{5}{5}+\frac{5}{5}-\frac{5}{7}+...+\frac{5}{21}-\frac{5}{23}\)

\(=5\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{21}-\frac{1}{23}\right)\)

\(=5\left(1-\frac{1}{23}\right)\)

\(=5.\frac{22}{23}\)

\(=\frac{110}{23}\)

Answer 2

\(A=\frac{5}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+......+\frac{1}{21}-\frac{1}{23}\right)\)

\(A=\frac{5}{2}.\left(1-\frac{1}{23}\right)\)

\(A=\frac{5}{2}.\frac{22}{23}\)

\(A=\frac{55}{23}\)

Answer 3

A.\(\frac{2}{5}\)=\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+............+\)\(\frac{2}{21.23}\)

A.\(\frac{2}{5}=1-\frac{1}{23}\)

A.\(\frac{2}{5}=\frac{21}{23}\)

A=\(\frac{21}{23}.\frac{5}{2}\)

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