1/n^(1/2)-1/(n+1)^(1/2)=[(n+1)^(1/2)-n^(1/2)]/[n^(1/2)*(n+1)^1/2]=1/{[n^(1/2)*(n+1)^1/2*[(n+1)^(1/2)+n^(1/2)]}lim=1/[2*n(3/2)]当n无穷大时,增加的n*1/[2*n(3/2)]趋于0,所以是收敛的.增加的单项乘以n(无穷)后仍然趋于0,就是收敛的.
