巧算(1+3)(1+3平方)(1+3四次方)(1+3八次方)(1+3十六次方)-2/1

问题描述:

巧算(1+3)(1+3平方)(1+3四次方)(1+3八次方)(1+3十六次方)-2/1

分子分母同时乘上(3-1)
[(3-1)(1+3)(1+3^2)(1+3^4)(1+3^8)(1+3^16)*2]/(3-1)
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)
=(3^8-1)(3^8+1)(3^16+1)
=(3^16-1)(3^16+1)
=3^32-1