举一反三
- 求下列幕级数的收敛半径与收敛域．[tex=5.643x2.714]ySadpvq7BrEZCGdcnD6+af/cnPy6ia97hD6rfpdbIi30RRCvZWX4IHwk0SrC9xQD[/tex]．
- 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]
- 确定下列级数的收敛半径与收敛域：[tex=3.929x3.429]VCAPAvn3gOPyP36rvxBwz8VT0IIKEZ4u2ulloLRpEeSuQxzh8+Qq4nKearoHhkjf[/tex]
- 求[tex=4.143x3.286]3PXegz5bAQsuTODB0U8KrJ5fQhmJUpPU1AcRYR69zJ8DpBhRaGFWylGKFnz6qn9I[/tex]的收敛半径与收敛域.
- 设正项级数[tex=2.714x2.714]ySadpvq7BrEZCGdcnD6+aevQSiUapl3qI6D/1lvgJVQ=[/tex]收敛，则下列级数中，一定收敛的是[input=type:blank,size:6][/input] . 未知类型：{'options': ['[tex=5.286x2.714]ySadpvq7BrEZCGdcnD6+aUSs8NjqGM34Pj0L/aWjPf5nwpc8Gxc46klh+uULINYq[/tex][tex=4.786x1.286]0IqZGXsQumQ8HVtPWCATrtiJCBHUv8/DIKQIwjftTCI=[/tex]', '[tex=3.571x2.714]ySadpvq7BrEZCGdcnD6+aSrhkX13cc9+5wstZa/wdPBrtZqNaznOw9czyCs260T4[/tex]', '[tex=2.929x2.714]ySadpvq7BrEZCGdcnD6+aXdjt7olXa1sOQ/uQAnHb9YfMOOvt9w4M+ygFFPEXpM3[/tex]', '[tex=5.071x2.714]ySadpvq7BrEZCGdcnD6+aXJu218uJmjxWnvA5oEiEDTma8mLHGCbClj8X9wIEyr2[/tex]'], 'type': 102}
内容
- 0
【1】求级数X^n/n^3的收敛域【2】求级数(2^n/n+1)*x^n的收敛半径
- 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
若已知级数[tex=3.714x3.286]WGu493lWbQkNjIXIJ06onT3QU0jn8OIdvbSEozq++L5iYU5MhSc0wTrCNvECtMFc[/tex] 的收敛半径为[tex=6.5x1.357]8WZN0goBGCBxHj8z0du2FBgWhVfUgmq9Pzh/8Sw4nTY=[/tex]. 试证级数 [tex=6.929x3.286]WGu493lWbQkNjIXIJ06onUhrA629m7A11jL1rVa4kmWH21E8JlR8KYWhCJznEEw9U3RA/R441vaWNWIygkauUA==[/tex]的收敛半径为[tex=7.571x2.786]xGuXb+WGabExcMy4WVzhLN8mjKojv7R2UqsYJrKBKwui3V8ncv9qmx8RA1F5HJcu7Tv34ISICAeBYbC2/o7srg==[/tex]
- 3
确定下列级数的收敛半径与收敛域：[tex=4.0x3.071]wI03c1jobBnuEHvblGcXj3kuT91IDrR4LIhJ/lSGd9+hPcYE0b2w/iprlBB5l3dH[/tex]
- 4
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].