Question

[Phạm Bảo Nhi]

4.1/8+1/24+1/48+1/80+1/120+1/168+1/224

''giúp mik với mik cảm ơn''

Answer 1

[Hiền Thương]

\(\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}+\dfrac{1}{168}+\dfrac{1}{224}\)

\(=\dfrac{1}{2\cdot4}+\dfrac{1}{4\cdot6}+\dfrac{1}{6\cdot8}+\dfrac{1}{8\cdot10}+\dfrac{1}{10\cdot12}+\dfrac{1}{12\cdot14}+\dfrac{1}{14\cdot16}\)

\(=\dfrac{1}{2}\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+\dfrac{2}{6\cdot8}+\dfrac{2}{8\cdot10}+\dfrac{2}{10\cdot12}+\dfrac{2}{12\cdot14}+\dfrac{2}{14\cdot16}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{14}-\dfrac{1}{16}\right)\)

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

\(=\dfrac{1}{2}\cdot\dfrac{7}{16}=\dfrac{7}{32}\)

Answer 2

[Phạm Bảo Nhi]

kết bn ko HIỀN THƯƠNG