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交错级数如何判断发散
更新时间: 2020-10-29 00:00:00  

交错级数的莱布尼茨定理是充分条件不是必要的,不满足该定理可能可以用别的判别法来判别,不能直接判定是发散的,但如果通项不以零为极限,则发散是肯定的。

交错级数是正项和负项交替出现的级数,形式满足a1-a2+a3-a4+.......+(-1)^(n+1)an+......,或者-a1+a2-a3+a4-.......+(-1)^(n)an,其中an>0。在交错级数中,常用莱布尼茨判别法来判断级数的收敛性,即若交错级数各项的绝对值单调递减且极限是零,则该级数收敛。此外,由莱布尼茨判别法可得到交错级数的余项估计。最典型的交错级数是交错调和级数。

关键词: 交错 级数 如何 判断 发散

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