Tính: A=1/5+1/45+1/117+1/221+…+1/2700. Giúp mik với. LOVE YOU 3000 19/09/2021 Bởi Autumn Tính: A=1/5+1/45+1/117+1/221+…+1/2700. Giúp mik với. LOVE YOU 3000
`A` `=` `\frac{1}{5}` `+` `\frac{1}{45}` `+` `\frac{1}{117}` `+` `\frac{1}{221}` `+…+` `\frac{1}{2700}` `=` `\frac{1}{1.5}` `+` `\frac{1}{5.9}` `+` `\frac{1}{9.13}` `+` `\frac{1}{13.17}` `+…+` `\frac{1}{50.54}` `=` `\frac{1}{4}“(\frac{4}{1.5}` `+` `\frac{4}{5.9}` `+` `\frac{4}{9.13}` `+` `\frac{4}{13.17}` `+…+` `\frac{4}{50.54})` `=` `\frac{1}{4}“(\frac{1}{1}-“\frac{1}{5}+“\frac{1}{5}-“\frac{1}{9}+“\frac{1}{9}-“\frac{1}{13}“+\frac{1}{13}-“\frac{1}{17}+…+“\frac{1}{50}-“\frac{1}{54})` `=` `\frac{1}{4}“(1-\frac{1}{54})` `=` `\frac{1}{4}.“\frac{53}{54}` `=` `\frac{53}{216}` Vậy `: ` `A=` `\frac{53}{216}` Bình luận
`A` `=` `\frac{1}{5}` `+` `\frac{1}{45}` `+` `\frac{1}{117}` `+` `\frac{1}{221}` `+…+` `\frac{1}{2700}`
`=` `\frac{1}{1.5}` `+` `\frac{1}{5.9}` `+` `\frac{1}{9.13}` `+` `\frac{1}{13.17}` `+…+` `\frac{1}{50.54}`
`=` `\frac{1}{4}“(\frac{4}{1.5}` `+` `\frac{4}{5.9}` `+` `\frac{4}{9.13}` `+` `\frac{4}{13.17}` `+…+` `\frac{4}{50.54})`
`=` `\frac{1}{4}“(\frac{1}{1}-“\frac{1}{5}+“\frac{1}{5}-“\frac{1}{9}+“\frac{1}{9}-“\frac{1}{13}“+\frac{1}{13}-“\frac{1}{17}+…+“\frac{1}{50}-“\frac{1}{54})`
`=` `\frac{1}{4}“(1-\frac{1}{54})`
`=` `\frac{1}{4}.“\frac{53}{54}`
`=` `\frac{53}{216}`
Vậy `: ` `A=` `\frac{53}{216}`