(2+1)•(2•2+1)•(2•2•2•2+1)……•(2•2•2快呀急!
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![(2+1)•(2•2+1)•(2•2•2•2+1)……•(2•2•2](/uploads/image/z/13854744-0-4.jpg?t=%EF%BC%882%2B1%EF%BC%89%26%238226%3B%EF%BC%882%26%238226%3B2%2B1%EF%BC%89%26%238226%3B%EF%BC%882%26%238226%3B2%26%238226%3B2%26%238226%3B2%2B1%EF%BC%89%E2%80%A6%E2%80%A6%26%238226%3B%EF%BC%882%26%238226%3B2%26%238226%3B2%26%23%E5%BF%AB%E5%91%80%E6%80%A5%21)
(2+1)•(2•2+1)•(2•2•2•2+1)……•(2•2•2快呀急!
(2+1)•(2•2+1)•(2•2•2•2+1)……•(2•2•2
快呀
急
!
(2+1)•(2•2+1)•(2•2•2•2+1)……•(2•2•2快呀急!
补上乘以1=(2-1) 这项.
然后不断用平方差公式
(2-1)*(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=(2^2-1)*(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=(2^4-1)*(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=(2^8-1)*(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=(2^16-1)*(2^16+1)(2^32+1)(2^64+1)
=(2^32-1)*(2^32+1)(2^64+1)
=(2^64-1)*(2^64+1)
=2^128-1