Question

利用数列极限的定义证明lim3n+1/2n+1=3/2

Answer 1

问：利用数列极限的定义证明lim3n+1/2n+1=3/2

答：设x＞0｜（3n+1）/（2n+1）-3/2｜=｜（6n+2）/2（2n+1）-（6n+3）/2（2n+1）｜=｜-1/2（2n+1）｜=1/2（2n+1）＜x

问：。。。看不懂

答：x＞1/（4x）-1/2取N=[1/（4x）-1/2]当n＞N，有｜（3n+1）/（2n+1）-3/2｜＜x

答：所以lim（3n+1）/（2n+1）=3/2

答：这个就是极限证明哦

答：所以lim（3n+1）/（2n+1）=lim（3+1/n）/（2+1/n）因为n趋于∞所以1/n=0所以lim（3n+1）/（2n+1）=3/2

答：方法二如上