Question

1、化简算式求值：（要有具体步骤）？

Answer 1

(2+1)(2^2+1)(2^4+1)(2^8+901)(2^16+1)(2^32+1)
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+901)(2^16+1)(2^32+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+901)(2^16+1)(2^32+1)
=(2^4-1)(2^4+1)(2^8+901)(2^16+1)(2^32+1)
=……………………………………
=2^64-1
n^2+(n(n+1))^2+(n+1)^2=(n(n+1)+1)^2
(道理嘛…………………………您把式子展开就知道了),8,(1):原式=[(2-1)(2+1)]*(2^2+1)(2^4+1)...(2^32+1)=[(2^2-)(2^2+1)](2^4+1)(2^8+1)(2^16+1)(2^32+1)=[(2^8-1)(2^8+1)](2^16+1)(2^32+1)=...=2^64-1;(2):规律是:n^2+[n(n+1)]^2+(n+1)^2=(n^2+n+1)^2.证明:左式-[n(n+1)]^2=n^2+...,1,1、化简算式求值：（要有具体步骤）
(2+1)(2^2+1)(2^4+1)(2^8+901)(2^16+1)(2^32+1)
2、观察下列式子：
1^2+(1x2)^2+2^2=9=3^2
2^2+(2x3)^2+3^2=49=7^2
3^2+(3x4)^2+4^2=169=13^2
……
用含n的等式（n为正整数）表示出来,并说明其中的道理.