由于ρ=n→+∞lim[a‹n+1›/a‹n›]=n→+∞lim[1/(2n+2))!]/[1/(2n)!]
=n→+∞lim[(2n)!/(2n+2)!]=n→+∞lim[(2n)!/(2n)!(2n+1)(2n+2)]
=n→+∞lim[1/(2n+1)(2n+2)]=0
故收敛半径R=1/ρ=∞,收敛区间为(-∞,+∞).
由于ρ=n→+∞lim[a‹n+1›/a‹n›]=n→+∞lim[1/(2n+2))!]/[1/(2n)!]
=n→+∞lim[(2n)!/(2n+2)!]=n→+∞lim[(2n)!/(2n)!(2n+1)(2n+2)]
=n→+∞lim[1/(2n+1)(2n+2)]=0
故收敛半径R=1/ρ=∞,收敛区间为(-∞,+∞).