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阿Q吧 > 判断下列级数的敛散性，并说明是条件收敛还是绝对收敛谢谢啦~~两题都要

判断下列级数的敛散性，并说明是条件收敛还是绝对收敛谢谢啦~~两题都要

2025-03-15 02:24:16

推荐回答（1个）

回答1：

第一个级数发散，因为一般项不趋向零，谈不上条件收敛
第二个级数一般项可化为sin(npi+pi/n)=(-1)^n sin(pi/n) 交错级数，一般项的绝对值sin(pi/n)单调趋向零，本身收敛。但取绝对值后，sin(pi/n)和pi/n比值趋向pi，因而与一般项为pi/n的级数同敛散，后者发散，故原级数条件收敛

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