用比较申敛法判定收敛性.1+(1+2)/(1+2²)+(1+3)/(1+3²)+...+(1+n²)/(1+n²)+...我是这么写的,请问错在哪里?an＝(1+n)/(1+n²)＜1/(1+n²)＜1/n²因为级数1/n²收敛,所以原级数收敛.但答

Question

用比较申敛法判定收敛性.1+(1+2)/(1+2²)+(1+3)/(1+3²)+...+(1+n²)/(1+n²)+...
我是这么写的,请问错在哪里?an＝(1+n)/(1+n²)＜1/(1+n²)＜1/n² 因为级数1/n²收敛,所以原级数收敛.但答案是an＞(1+n)/(n+n²)＝1/n,而级数1/n发散,所以原级数发散.

Answer 1

an＝(1+n)/(1+n²)＜1/(1+n²)＜1/n² 不成立,因为an＝(1+n)/(1+n²)﹥1/(1+n²)＜1/n² ,