(3+1)(3²+1)(3的四次方+1)(3的八次方+1)...(3的十次方+1)
问题描述:
(3+1)(3²+1)(3的四次方+1)(3的八次方+1)...(3的十次方+1)
答
原式通过乘上1/2×(3-1),可以不断的形成平方差.原式=1/2×(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1) =1/2×(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1) =1/2×(3^4-1)(3^4+1)(3^8+1)(3^16+1) =1/2×(3^8-1)(3^8+1)(3^16+1...