设an=1+1/2+1/3+1/4+...+1/3n-1(n∈N*),则a(n+1)-an=快啊,好的给分!

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/20 08:13:22
设an=1+1/2+1/3+1/4+...+1/3n-1(n∈N*),则a(n+1)-an=快啊,好的给分!

设an=1+1/2+1/3+1/4+...+1/3n-1(n∈N*),则a(n+1)-an=快啊,好的给分!
设an=1+1/2+1/3+1/4+...+1/3n-1(n∈N*),则a(n+1)-an=
快啊,好的给分!

设an=1+1/2+1/3+1/4+...+1/3n-1(n∈N*),则a(n+1)-an=快啊,好的给分!
a(n+1) = 1+1/2+1/3+.+1/(3n-1)+...+1/[3(n+1)-1]
= 1+1/2+1/3+.+1/(3n-1)+...+1/(3n+2)
= 1+1/2+1/3+.+1/(3n-1)+1/3n+1/(3n+1)+1/(3n+2)
an = 1+1/2+1/3+.+1/(3n-1)
a(n+1) - an = 1/3n + 1/(3n+1) + 1/(3n+2)

an+1=1+1/2+1/3+1/4+...+1/(3n+2)
an+1-an=1/(3n)+1/(3n+1)+1/(3n+2)