级数的敛散性级数如下图,判断其是否收敛,如果收敛是条件收敛还是绝对收敛?
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级数的敛散性
级数如下图,判断其是否收敛,如果收敛是条件收敛还是绝对收敛?
![](http://img.wesiedu.com/upload/8/84/8844fa0bb3e6ff3dbdd2ac075e61f609.jpg)
级数如下图,判断其是否收敛,如果收敛是条件收敛还是绝对收敛?
![](http://img.wesiedu.com/upload/8/84/8844fa0bb3e6ff3dbdd2ac075e61f609.jpg)
![级数的敛散性级数如下图,判断其是否收敛,如果收敛是条件收敛还是绝对收敛?](/uploads/image/z/17879390-62-0.jpg?t=%E7%BA%A7%E6%95%B0%E7%9A%84%E6%95%9B%E6%95%A3%E6%80%A7%E7%BA%A7%E6%95%B0%E5%A6%82%E4%B8%8B%E5%9B%BE%2C%E5%88%A4%E6%96%AD%E5%85%B6%E6%98%AF%E5%90%A6%E6%94%B6%E6%95%9B%2C%E5%A6%82%E6%9E%9C%E6%94%B6%E6%95%9B%E6%98%AF%E6%9D%A1%E4%BB%B6%E6%94%B6%E6%95%9B%E8%BF%98%E6%98%AF%E7%BB%9D%E5%AF%B9%E6%94%B6%E6%95%9B%3F)
i think it is convergent and it converges absoluely.
we use the alternating series test, that is if |fn| is decreasing and the limit of |fn|=0 when n->infinity ,then the series of fn is absolutely convergent.
|fn|=1/(nln(n+1)) which is decreasing obviously and equals 0 when n approaches infinity.
we use the alternating series test, that is if |fn| is decreasing and the limit of |fn|=0 when n->infinity ,then the series of fn is absolutely convergent.
|fn|=1/(nln(n+1)) which is decreasing obviously and equals 0 when n approaches infinity.