`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}`
