思路：
①分组：按照author，月份进行分组；
②各计算值：每月新增粉丝=当月内粉丝变化数之和（注意把2变为-1）；总播放量用count即可；累计粉丝新增数用窗口函数sum(每月新增粉丝数)over(partition by author order by 月份)，注意要加order by才能逐行累加；
③筛选条件：年份为2021。
题目瑕疵：题中所说截至当前累计粉丝数应该为 2021年总新增粉丝数。因为作者如果2020年及以前就有粉丝累计，那么就需要增加2020年及以前分数数的计算代码，跟题意不符。
select author, date_format(end_time,'%Y-%m') as `month`, 
round(sum(if(if_follow=2,-1,if_follow))/count(author),3) as fans_growth_rate,
sum(sum(if(if_follow=2,-1,if_follow)))over(partition by author order by date_format(end_time,'%Y-%m')) as total_fans
from tb_user_video_log left join tb_video_info using(video_id)
where year(end_time)=2021
group by author, date_format(end_time,'%Y-%m')
order by author, total_fans