设原级数是∑an,其中an=(n+3) / [n(n+1)(n+2)]
构造级数∑bn ,其中bn=1/(n^2)
lim {n->无穷大} an/bn =lim {n->无穷大} [(n^2)(n+3)] / [n(n+1)(n+2)]
=1
由于∑bn收敛,所以原级数也收敛
用比较判别法或其极限形式判定级数的敛散性
设原级数是∑an,其中an=(n+3) / [n(n+1)(n+2)]
构造级数∑bn ,其中bn=1/(n^2)
lim {n->无穷大} an/bn =lim {n->无穷大} [(n^2)(n+3)] / [n(n+1)(n+2)]
=1
由于∑bn收敛,所以原级数也收敛