Question

求级数的收敛性,n^2+1/(n^2+3)(n^2+2),n从1到无穷

Answer 1

若n为正整数,则题中级数为正项级数；由于[(1＋n^2)/(1＋n^3)]^2＜[(n^2＋n^2)/(n^3)],即[(1＋n^2)/(1＋n^3)]^2＜4/(n^2),级数4/(n^若n为正整数,则题中级数为正项级数；由于[(1＋n^2)/(1＋n^3)]^2＜[(n^2＋n^2)/(n^3)],即[(1＋n^2)/(1＋n^3)]^2＜4/(n^2),级数4/(n^2)收敛,所以原级数也收敛.2)收敛,所以原级数也收敛.

Answer 2

Un<(n²+1)/(n²*n²)=（1+1/n²)/n²， 后者收敛
因此级数收敛