举一反三
- 若幂级数[tex=6.143x2.714]LCs/jzl+nr3KBTJXBn4IiayGbO3mHEyJVGDR2iuZq51jIMcmvWJ08UlShJwZbuBg[/tex]在点[tex=2.5x2.0]LGMw/eiuBwl+2IKDs8M9FRK5DUCoNb82pQFDgPTiIMo=[/tex]处条件收敛，则该级数的收敛半径[tex=1.786x1.286]Eel/43QVL0PzCy59mNb01g==[/tex][input=type:blank,size:4][/input]
- 若幂级数[img=101x60]1803c234e14df38.png[/img]在x=3处条件收敛，则收敛半径R= A: 2 B: 1 C: 5 D: 6 E: 3 F: 4 G: 8 H: 9 I: 7 J: 0
- 设幂级数[tex=6.143x2.786]1VOO0Jwm6ojCyMMTUqy4YCvc84RmfkXhUbrwTr96Y/gBsYex1cEAkEGx7dAaY/Lu[/tex]在[tex=1.857x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex]收敛,在[tex=1.857x1.0]X7etWab1J10Xwqu65uIXXQ==[/tex]发散,试确定该幂级数的收敛域并说明理由.
- 若幂级数[tex=5.643x3.286]WGu493lWbQkNjIXIJ06onS66TpY1ESvHjC6mTpTtrCqRO4haaSvoJ4IeUgRisTQd[/tex]在 [tex=2.643x1.143]zT2NoPHqm8oWXH3Qf5JfEg==[/tex] 处收敛,则此级数在 [tex=1.857x1.0]X7etWab1J10Xwqu65uIXXQ==[/tex] 处[input=type:blank,size:4][/input][tex=1.571x1.357]t4j8DiUnyf9QhxbEEfhEow==[/tex]条件收敛[tex=1.571x1.357]6ZdvBUUXTfu1lpc1bzYo0Q==[/tex]绝对收敛[tex=1.5x1.357]X5iBhM5NuOpB4RU5sidyMA==[/tex]发散[tex=1.643x1.357]wpzMUyk23s46CrIX9IcgFw==[/tex]收敛性不确定
- 设幂级数[tex=3.714x2.714]ySadpvq7BrEZCGdcnD6+afbHwFuEUnhNinvU4CftdSuHWLAVyPJO10xmerPasF7V[/tex]与[tex=3.643x2.714]ySadpvq7BrEZCGdcnD6+aZYQmThLWn62+xEp10r+Yje3wMSRdU+94GC79UQKgKMF[/tex]的收敛半径分别为[tex=1.5x2.214]Q6hn/+Ier4ve0s3ZRWtaH6bVPJJ+1266FlpM7Ks0ov8=[/tex]与[tex=0.714x2.0]BQ7Y89Ue+4zhZqRGXqiH6Qg3j168kuR7xZeu/fPVLEY=[/tex]，则幂级数[tex=3.929x2.714]ySadpvq7BrEZCGdcnD6+aQw54ipYZtEnro1NbjSVrvikdozSYOFq0TCnA9BmSohRFetstY/HAmMzqNFeWgeRoA==[/tex]的收敛半径为 未知类型：{'options': ['5', '[tex=1.5x2.214]Q6hn/+Ier4ve0s3ZRWtaH6bVPJJ+1266FlpM7Ks0ov8=[/tex]', '[tex=0.714x2.0]BQ7Y89Ue+4zhZqRGXqiH6Qg3j168kuR7xZeu/fPVLEY=[/tex]', '[tex=0.714x2.0]qGMbJXQyvs09X13cJA8QYaOiHO2FnSEHKnyF5mow6js=[/tex]'], 'type': 102}
内容
- 0
设幂级数[tex=3.643x3.286]WGu493lWbQkNjIXIJ06onV6IZmMDrYShNGcPME8shwWKH5T1GYVkFqbYkQtvxgXS[/tex]的收敛半径为[tex=1.143x1.214]WB5oUFU97imVoOqmwwnMtg==[/tex], 而[tex=3.5x3.429]UU1qstNjdmzg7TFKGbeGXsJXpXGu4k7SZ5Pl374mxwk=[/tex]的收敛半径为[tex=1.143x1.214]akFdfHl3PdcRxRUQleHWdA==[/tex].若把幂级数[tex=6.214x3.286]WGu493lWbQkNjIXIJ06oneLZcJFoQ3BGITMlybWara2JPRKknBTl8nFXbTZweoPu0vBt34L3pxIcH/n/A76GVQ==[/tex]的收敛半径记为[tex=0.786x1.0]AOSTmhvIsOwsdZlGoks7dg==[/tex], 证明:[tex=7.286x1.357]/Ormn0xncvBSYPuYSYE8Zf4KYeLykBmiGoKt1A6m2PKY9SnlqBOnZ0Or2B4jHlMy[/tex]
- 1
设幂级数[tex=3.643x3.286]WGu493lWbQkNjIXIJ06onV6IZmMDrYShNGcPME8shwWKH5T1GYVkFqbYkQtvxgXS[/tex]的收敛半径为[tex=1.143x1.214]WB5oUFU97imVoOqmwwnMtg==[/tex], 而[tex=3.5x3.429]UU1qstNjdmzg7TFKGbeGXsJXpXGu4k7SZ5Pl374mxwk=[/tex]的收敛半径为[tex=1.143x1.214]akFdfHl3PdcRxRUQleHWdA==[/tex].若把幂级数[tex=6.214x3.286]WGu493lWbQkNjIXIJ06oneLZcJFoQ3BGITMlybWara2JPRKknBTl8nFXbTZweoPu0vBt34L3pxIcH/n/A76GVQ==[/tex]的收敛半径记为[tex=0.786x1.0]AOSTmhvIsOwsdZlGoks7dg==[/tex], 证明:当 [tex=3.571x1.214]UwYj7//Vchh6BHOGv2BcaKcde3PLpSYYPS7ulmfNRD8=[/tex]时, [tex=7.071x1.357]KREFzHfNLktQlPN7y/7IF7Vgs1XtsMgQQ7IJi/yWGRM9VyMyXJwThLHQUItzCk3I[/tex].
- 2
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].
- 3
求幂级数的收敛半径与收敛区域.[tex=4.0x1.5]Xdav2khU6mDVwWx3MkeDDjPfsDmz2505cx6KRPCh8Jk=[/tex],[tex=4.786x1.286]qY2WXCNTTtm52rrZdeYoxQ==[/tex].
- 4
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.