21²+22²+28²+...+31×32+32×33+...+38×39前面的算是打错了,应该是:21²+22²+...+28²+31×32+32×33+...+38×39
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 14:19:11
![21²+22²+28²+...+31×32+32×33+...+38×39前面的算是打错了,应该是:21²+22²+...+28²+31×32+32×33+...+38×39](/uploads/image/z/6882885-45-5.jpg?t=21%26%23178%3B%2B22%26%23178%3B%2B28%26%23178%3B%2B...%2B31%C3%9732%2B32%C3%9733%2B...%2B38%C3%9739%E5%89%8D%E9%9D%A2%E7%9A%84%E7%AE%97%E6%98%AF%E6%89%93%E9%94%99%E4%BA%86%EF%BC%8C%E5%BA%94%E8%AF%A5%E6%98%AF%EF%BC%9A21%26%23178%3B%2B22%26%23178%3B%2B...%2B28%26%23178%3B%2B31%C3%9732%2B32%C3%9733%2B...%2B38%C3%9739)
21²+22²+28²+...+31×32+32×33+...+38×39前面的算是打错了,应该是:21²+22²+...+28²+31×32+32×33+...+38×39
21²+22²+28²+...+31×32+32×33+...+38×39
前面的算是打错了,应该是:21²+22²+...+28²+31×32+32×33+...+38×39
21²+22²+28²+...+31×32+32×33+...+38×39前面的算是打错了,应该是:21²+22²+...+28²+31×32+32×33+...+38×39
应用数列求和公式:
1^2+2^2+3^2+.+n^2=[n*(n+1)*(2n+1)]/6
1+2+3+.+n=(1+n)*n/2
31×32+32×33+...+38×39
=31*(31+1)+32*(32+1)+.+38*(38+1)
=(31^2+32^2+.+38^2)+(31+32+.+38)
原题:21²+22²+...+28²+31×32+32×33+...+38×39
=(21^2+22^2+.+28^2+31^2+32^2+.+38^2)+(31+32+.+38)
=(1^2+2^2+.+38^2)-(1^2+2^2+.+20^2)-(29^2+30^2)+(31+32+.+38)
=38*(38+1)*(2*38+1)/6-20*(20+1)*(2*20+1)/6-(841+900)+(31+38)*8/2
=19019-2870-1741+276
=14684
发错了吧。23的平方有没有。平方是加到30吗?