Question

级数1/(n(n-1))是收敛还是发散

Answer 1

收敛

1/(n(n-1))=1/(n-1)-1/n

∑1/(n(n-1))=(1-1/2)+(1/2-1/3)+...+(1/(n-1)-1/n)=1-1/n

取极限为1

极限存在,所以收敛