证明：几何级数[tex=2.643x2.714]LCs/jzl+nr3KBTJXBn4IiUf4h3itRUCPU9m7ZR5VCxY=[/tex]具有以下性质：在[tex=4.643x1.357]oK1mqtcwILcLnZ+WS8uml65wZZjroUY20BWyjtpuwIs=[/tex]内，级数一致收敛.
举一反三
- 证明：几何级数[tex=2.643x2.714]LCs/jzl+nr3KBTJXBn4IiUf4h3itRUCPU9m7ZR5VCxY=[/tex]具有以下性质：在[tex=2.857x1.357]9Mp6NtTOllagZJ7zLzgTJQ==[/tex]内，级数不一致收敛.
- 证明：几何级数[tex=2.643x2.714]LCs/jzl+nr3KBTJXBn4IiUf4h3itRUCPU9m7ZR5VCxY=[/tex]具有以下性质：当[tex=2.857x1.357]9Mp6NtTOllagZJ7zLzgTJQ==[/tex]时，级数收敛.
- 设级数[tex=3.571x2.714]LCs/jzl+nr3KBTJXBn4IiTaMdvoS/p/hGL/Jv9ntegzmzbVBv3v1HeKEgBlLcyLM[/tex]的收敛半径为[tex=7.286x1.357]sTdvH6zX0iZNqILTrUec+Q==[/tex]，证明：级数[tex=7.143x2.714]LCs/jzl+nr3KBTJXBn4IiVrR/a63aRDgwm6Ulx0DCkqQZXUGezi8qQqRicSofTkUWyb3f6mqFTz2twehW0bB7Q==[/tex]的收敛半径为[tex=7.714x2.786]88n1NtKriG0YM72QT5w50ARKMC3GTCC7OGxgHAYlBdhewQuMEfErAwKQ9wpi7IxVHJewFuEn04JodLhBCFDNBA==[/tex].
- 设正项级数 [tex=2.643x1.357]txD3QEY3vcweZJuJhQiJqQ==[/tex]收敛 ,证明级数[tex=5.571x1.357]IAsk7sFNw9hFKuiKwVEkUcwQ1mswCRh67nB4qUbaTe3LRdfGdjm6zwnVDhNGrTr+[/tex] 也收敛.
- 求证：级数[tex=4.143x3.286]3PXegz5bAQsuTODB0U8KrO8dE2QFyGzTKIgAWyUOAjW2NnK99u1z9bgI+kTvhzvW[/tex]在[tex=2.857x1.357]bxkuEf5OdjtfMlwpIXZhFYFm4mzHICAh/+PdGm82/Ds=[/tex]上发散；在[tex=2.857x1.357]W2UvKR01GUJgbq0KdXYJYQ==[/tex]内绝对收敛且内闭 一致收敛，但非一致收敛。