Question

1/n(n+2)的收敛性

Answer 1

1/n(n+2)=1/2*[1/n-1/(n+2)]

所以S=lim1/2*[1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+……+1/(n-1)-1/(n+1)+1/n-1/(n+2)]

=1/2*lim[1+1/2-1/(n+1)-1/(n+2)]

=1/2*3/2

收敛