求(3+1)(3^2+1)(3^4+1).(3^32+1)-2分之3的64次方的值
问题描述:
求(3+1)(3^2+1)(3^4+1).(3^32+1)-2分之3的64次方的值
答
(3+1)(3^2+1)(3^4+1).(3^32+1)
=1/2×(3-1)(3+1)(3^2+1)(3^4+1).(3^32+1)
=1/2×(3^2-1)(3^2+1)(3^4+1).(3^32+1)
=1/2×(3^4-1)(3^4+1).(3^32+1)
=……
=1/2(3^32-1)(3^32+1)
=1/2(3^64-1)
=1/2·3^64-1/2
故原式=1/2·3^64-1/2-1/2·3^64=-1/2