计算:1×2²+2×3²+3×4²+...+18×19²+19×20²提示:1²+2²+3²+...+n²=1/6 n(n+1)(2n+1),1³+2³+...+n³=1/4 n²(n+1)² 这是原题,写得好的给分.
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/20 19:07:27
![计算:1×2²+2×3²+3×4²+...+18×19²+19×20²提示:1²+2²+3²+...+n²=1/6 n(n+1)(2n+1),1³+2³+...+n³=1/4 n²(n+1)² 这是原题,写得好的给分.](/uploads/image/z/364406-14-6.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A1%C3%972%26%23178%3B%2B2%C3%973%26%23178%3B%2B3%C3%974%26%23178%3B%2B...%2B18%C3%9719%26%23178%3B%2B19%C3%9720%26%23178%3B%E6%8F%90%E7%A4%BA%EF%BC%9A1%26%23178%3B%2B2%26%23178%3B%2B3%26%23178%3B%2B...%2Bn%26%23178%3B%3D1%2F6+n%28n%2B1%29%282n%2B1%29%2C1%26%23179%3B%2B2%26%23179%3B%2B...%2Bn%26%23179%3B%3D1%2F4+n%26%23178%3B%28n%2B1%29%26%23178%3B+%E8%BF%99%E6%98%AF%E5%8E%9F%E9%A2%98%2C%E5%86%99%E5%BE%97%E5%A5%BD%E7%9A%84%E7%BB%99%E5%88%86.)
计算:1×2²+2×3²+3×4²+...+18×19²+19×20²提示:1²+2²+3²+...+n²=1/6 n(n+1)(2n+1),1³+2³+...+n³=1/4 n²(n+1)² 这是原题,写得好的给分.
计算:1×2²+2×3²+3×4²+...+18×19²+19×20²
提示:1²+2²+3²+...+n²=1/6 n(n+1)(2n+1),1³+2³+...+n³=1/4 n²(n+1)²
这是原题,写得好的给分.
计算:1×2²+2×3²+3×4²+...+18×19²+19×20²提示:1²+2²+3²+...+n²=1/6 n(n+1)(2n+1),1³+2³+...+n³=1/4 n²(n+1)² 这是原题,写得好的给分.
1×2²+2×3²+3×4²+...+18×19²+19×20²
=(2-1)×2²+(3-1)×3²+(4-1)×4²+...+(19-1)×19²+(20-1)×20²
=(1³+2³+...+20³)-1-(1²+2²+3²+...+20²)+1
=1/4x20²x21²-1/6x20x21x41
=1/4x400x441-2870
=44100-2870
=41230