计算(2+1)×(22+1)×(24+1)×(28+1)×(216+1)×(232+1)+1.
问题描述:
计算(2+1)×(22+1)×(24+1)×(28+1)×(216+1)×(232+1)+1.
答
原式=(2-1)×(2+1)×(22+1)×(24+1)×(28+1)×(216+1)×(232+1)+1
=(22-1)×(22+1)×(24+1)×(28+1)×(216+1)×(232+1)+1
=(24-1)×(24+1)×(28+1)×(216+1)×(232+1)+1
=(28-1)×(28+1)×(216+1)×(232+1)+1
=(216-1)×(216+1)×(232+1)+1
=(232-1)×(232+1)+1
=264-1+1
=264.