计算2²+4²+6²+8²+………+100²的值.
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/02 18:37:29
计算2²+4²+6²+8²+………+100²的值.
![计算2²+4²+6²+8²+………+100²的值.](/uploads/image/z/11875673-65-3.jpg?t=%E8%AE%A1%E7%AE%972%26%23178%3B%2B4%26%23178%3B%2B6%26%23178%3B%2B8%26%23178%3B%2B%E2%80%A6%E2%80%A6%E2%80%A6%2B100%26%23178%3B%E7%9A%84%E5%80%BC.)
1^2+2^2+3^2+…+n^2=n(n+1)(2n+1)/6
2²+4²+6²+8²+………+100²
=4*(1²+2²+3²+4²+………+50²)
=4*50*(50+1)*(100+1)/6
=171700
2²+4²+6²+8²+………+100²
=4*(1²+2²+3²+4²+………+50²)
=4*50*(50+1)*(100+1)/6
=171700
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