高等数学研究
高等數學研究
고등수학연구
STUDIES IN COLLEGE MATHEMATICS
2012年
3期
6-8
,共3页
数列%调和级数%歌拉常数%收敛性
數列%調和級數%歌拉常數%收斂性
수렬%조화급수%가랍상수%수렴성
sequence%harmonic series%Euler's constant%convergence
介绍数e与定义它的两个数列的单调性的一种简洁证明，给出由调和级数前n项之和与ln n之差所构成的数列收敛于欧拉常数的4种证明，并据此导出几个常见数列的极限及一个收敛性定理．
介紹數e與定義它的兩箇數列的單調性的一種簡潔證明，給齣由調和級數前n項之和與ln n之差所構成的數列收斂于歐拉常數的4種證明，併據此導齣幾箇常見數列的極限及一箇收斂性定理．
개소수e여정의타적량개수렬적단조성적일충간길증명，급출유조화급수전n항지화여ln n지차소구성적수렬수렴우구랍상수적4충증명，병거차도출궤개상견수렬적겁한급일개수렴성정리．
This paper introduces a simple way to verify the monotonicity of two sequences defining e, and gathers four ways to show that the difference of the partial sum S. of harmonic series and lnn converges to the Euler＇s constant C. Limits of some related sequences are derived and a convergence theorem of sequences is summarized.
