计算:10³+11³+12³+…+30³
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 20:32:38
![计算:10³+11³+12³+…+30³](/uploads/image/z/5548003-43-3.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A10%26%23179%3B%2B11%26%23179%3B%2B12%26%23179%3B%2B%E2%80%A6%2B30%26%23179%3B)
计算:10³+11³+12³+…+30³
计算:10³+11³+12³+…+30³
计算:10³+11³+12³+…+30³
根据公式
1³+2³+3³+…+n³=[(1/2)n(n+1)]²有:
10³+11³+12³+…+30³=[(1/2)×30×(30+1)]²-[(1/2)×9×(9+1)]²
=42840
10³+11³+12³+…+30³
=1^3+2^3+。。。+30^3-(1^3+2^3+...+9^3)
=30^2(30+1)^2/4-9^2*(9+1)^2/4
=1/4(30^2*31^2-9^2*10^2)
=1/4*(930+90)(930-90)
=255*840
=214200
10³+11³+12³+…+30³
=(1+2+...+30)^2-(1+2+...+9)^2
=216225-2025
=214200