Question

Tính S = 1/5 x 9 + 1/9 x 13 + 1/13 x 17+ ........+ 1/41 x 45

Answer 1

\(4.S=\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{41.45}\)

\(4S=\frac{1}{5}-\frac{1}{6}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{41}-\frac{1}{45}\)

\(4S=\frac{1}{5}-\frac{1}{45}=\frac{8}{45}\)

\(S=\frac{8}{45}:4=\frac{2}{45}\)

Answer 2

\(S=\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+...+\frac{1}{41.45}\)

\(\Rightarrow4S=\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{41.45}\)

\(\Rightarrow4S=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{41}-\frac{1}{45}\)

\(\Rightarrow4S=\frac{1}{5}-\frac{1}{45}=\frac{8}{45}\Rightarrow S=\frac{8}{45}:4=\frac{2}{45}\)

~ Hok tốt ~