Question

级数 柯西收敛准则∞ ∑ （ 1/(2n+1)+1/(2n+2) ）n=0由级数柯西收敛准则判断敛散性?

Answer 1

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.