作业帮解数学题[(2^3-1)(3^3-1)...100^3-1)]/[(2^3+1)(3^3+1)...(100^3+1)](
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/04 17:17:05
![解数学题[(2^3-1)(3^3-1)...100^3-1)]/[(2^3+1)(3^3+1)...(100^3+1)](](/uploads/image/z/12523034-2-4.jpg?t=%E8%A7%A3%E6%95%B0%E5%AD%A6%E9%A2%98%5B%282%5E3-1%29%283%5E3-1%29...100%5E3-1%29%5D%2F%5B%282%5E3%2B1%29%283%5E3%2B1%29...%28100%5E3%2B1%29%5D%28)
解数学题[(2^3-1)(3^3-1)...100^3-1)]/[(2^3+1)(3^3+1)...(100^3+1)](
解数学题[(2^3-1)(3^3-1)...100^3-1)]/[(2^3+1)(3^3+1)...(100^3+1)](
解数学题[(2^3-1)(3^3-1)...100^3-1)]/[(2^3+1)(3^3+1)...(100^3+1)](
上式=[(2-1)(2^2+1^2+1*2)(3-1)(3^2+1^2+1*3)...(100-1)(100^2+1^2+1*100)]/[(2+1)(2^2+1^2-1*2)(3+1)(3^2+1^2-1*3)...(100+1)(100^2+1^2-1*100)]
把各个括号里的数算出来最后消得
=[1*2*(100^2+1^2+1*100)]/3*100*101=3367/5050