判别级数∑[1/(2n+1)+1/(2n+2)]的敛散性用不着柯西收敛准则,用比较判别法足矣：因lim(n→∞)[1/(2n+1)+1/(2n+2)]/(1/n)= lim(n→∞)[1/(2+1/n)+1/(2+2/n)]= 1/2+1/2 = 1,而级数 ∑(1/n) 发散,据比较判别法知原级数发散.
