Question

\(S=\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+...+\frac{1}{224}\)

Các bạn giúp mình nhé !

Answer 1

\(S=\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+...+\frac{1}{224}\)

\(S=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{14.16}\)

\(2S=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{14.16}\)

\(2S=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{16}\)

\(2S=\frac{1}{2}-\frac{1}{16}\)

\(S=\frac{7}{16}:2=\frac{7}{32}\)

Ủng hộ mk nha !!! ^_^

Answer 2

\(S=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{14.16}\)

\(S=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{16}\)

\(S=\frac{1}{2}-\frac{1}{16}\)

\(S=\frac{7}{16}\)

Answer 3

\(S=\frac{1}{8}+\frac{1}{24}+...+\frac{1}{224}\)

\(\Rightarrow\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{14.16}\)

\(\Rightarrow\frac{1}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{14.16}\right)\)

\(\Rightarrow\frac{1}{2}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{14}-\frac{1}{16}\right)\)

\(\Rightarrow\frac{1}{2}\left(1-\frac{1}{16}\right)\)

\(\Rightarrow\frac{1}{2}.\frac{15}{16}\)\(\Rightarrow S=\frac{15}{32}\)

Answer 4

A đù làm nhầm =)) :v

Answer 5

\(S=\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+....+\frac{1}{224}\)

\(=\frac{1}{2.4}+\frac{1}{4.6}+....+\frac{1}{14.16}\)

\(=\frac{1}{2}\left(\frac{2}{2.4}+....+\frac{2}{14.16}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{4}+\frac{1}{4}-......+\frac{1}{14}-\frac{1}{16}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{16}\right)\)

\(=\frac{7}{32}\)

Answer 6

7/32 nhe

Answer 7

\(S=\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+....+\frac{1}{224}\)

\(S=\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+\frac{1}{6\cdot8}+.....+\frac{1}{14\cdot16}\)

\(2S=\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+.....+\frac{2}{14\cdot16}\)

\(2S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+.....+\frac{1}{14}-\frac{1}{16}\)

\(2S=1-\frac{1}{16}\)

\(S=\frac{15}{16}:2\)

\(S=\frac{15}{32}\)