乘以(2-1),再利用平方差公式!类似题目亦如此!
(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)……(2^512+1)+1
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)……(2^512+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)……(2^512+1)+1
……
=(2^512-1)(2^512+1)+1
=2^1024-1+1
=2^1024
2+1)(2∧2+1)(2∧4+1)(2∧8+1)(2∧16+1)……(2∧512+1)+1
2+1)(2∧2+1)(2∧4+1)(2∧8+1)(2∧16+1)……(2∧512+1)+1
数学人气:574 ℃时间:2020-04-15 01:52:16
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