平方差公式
1
(2+1)(2^2+1)(2^4+1)…(2^2n+1)
=(2-1)(2+1)(2^2+1)(2^4+1)…(2^2n+1)
=(2^2-1)(2^2+1)(2^4+1)…(2^2n+1)
=(2^4-1)(2^4+1)…(2^2n+1)
=(2^8-1)(2^8+1)…(2^2n+1)
=……
=2^4n-1 [2的4n次方减1]
2
2(3+1)(3^2+1)…(3^2002+1)
=(3-1)(3+1)(3^2+1)…(3^2002+1)
=(3^2-1)(3^2+1)…(3^2002+1)
=……
=3^4004-1
。 全部
1
(2+1)(2^2+1)(2^4+1)…(2^2n+1)
=(2-1)(2+1)(2^2+1)(2^4+1)…(2^2n+1)
=(2^2-1)(2^2+1)(2^4+1)…(2^2n+1)
=(2^4-1)(2^4+1)…(2^2n+1)
=(2^8-1)(2^8+1)…(2^2n+1)
=……
=2^4n-1 [2的4n次方减1]
2
2(3+1)(3^2+1)…(3^2002+1)
=(3-1)(3+1)(3^2+1)…(3^2002+1)
=(3^2-1)(3^2+1)…(3^2002+1)
=……
=3^4004-1
。
收起
