Question

Answer 1

b: Ta có: \(N=\frac{5}{2\times3}-\frac{7}{3\times4}+\frac{9}{4\times5}-\frac{11}{5\times6}+\cdots-\frac{51}{25\times26}+\frac{53}{26\times27}\)

\(=\frac12+\frac13-\frac13-\frac14+\frac14+\frac15-\frac15-\frac16+\cdots-\frac{1}{25}-\frac{1}{26}+\frac{1}{26}+\frac{1}{27}\)

\(=\frac12+\frac{1}{27}=\frac{29}{54}\)

Answer 2

b: Ta có: \(N=\frac{5}{2\times3}-\frac{7}{3\times4}+\frac{9}{4\times5}-\frac{11}{5\times6}+\cdots-\frac{51}{25\times26}+\frac{53}{26\times27}\)

\(=\frac12+\frac13-\frac13-\frac14+\frac14+\frac15-\frac15-\frac16+\cdots-\frac{1}{25}-\frac{1}{26}+\frac{1}{26}+\frac{1}{27}\)

\(=\frac12+\frac{1}{27}=\frac{29}{54}\)