式子(2^3-1)(3^3-1)(4^3-1)...(100^3-1)/(2^+1)(3^3+1)(4^3+1)...(100^3+1)的值

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 15:50:00
式子(2^3-1)(3^3-1)(4^3-1)...(100^3-1)/(2^+1)(3^3+1)(4^3+1)...(100^3+1)的值

式子(2^3-1)(3^3-1)(4^3-1)...(100^3-1)/(2^+1)(3^3+1)(4^3+1)...(100^3+1)的值
式子(2^3-1)(3^3-1)(4^3-1)...(100^3-1)/(2^+1)(3^3+1)(4^3+1)...(100^3+1)的值

式子(2^3-1)(3^3-1)(4^3-1)...(100^3-1)/(2^+1)(3^3+1)(4^3+1)...(100^3+1)的值
(2^3-1)(3^3-1)(4^3-1)...(100^3-1)/(2^+1)(3^3+1)(4^3+1)...(100^3+1)
=(2-1)(2^2+2+1)(3-1)(3^2+3+1)(4-1)(4^2+4+1)……(100-1)(100^2+100+1)/(2+1)(2^2-2+1)(3+1)(3^2-3+1)(4+1)(4^2-4+1)……(100+1)(100^2-100+1)
=1·2·3·……·99·7·13·……·10101/3·4·7·……·101·3·7·……·9901
=1/4