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=3^22^2+(2x3)^2+3^2=49=7^23^2+(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
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![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=3^22^2+(2x3)^2+3^2=49=7^23^2+(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](/uploads/image/z/7630456-40-6.jpg?t=1%E3%80%81%E5%8C%96%E7%AE%80%E7%AE%97%E5%BC%8F%E6%B1%82%E5%80%BC%EF%BC%9A%EF%BC%88%E8%A6%81%E6%9C%89%E5%85%B7%E4%BD%93%E6%AD%A5%E9%AA%A4%EF%BC%89%282%2B1%29%282%5E2%2B1%29%282%5E4%2B1%29%282%5E8%2B901%29%282%5E16%2B1%29%282%5E32%2B1%292%E3%80%81%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E5%BC%8F%E5%AD%90%EF%BC%9A1%5E2%2B%281x2%29%5E2%2B2%5E2%3D9%3D3%5E22%5E2%2B%282x3%29%5E2%2B3%5E2%3D49%3D7%5E23%5E2%2B%283x4%29%5E2%2B4%5E2%3D169%3D13%5E2%E2%80%A6%E2%80%A6%E7%94%A8%E5%90%ABn%E7%9A%84%E7%AD%89%E5%BC%8F%EF%BC%88n%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%EF%BC%89%E8%A1%A8%E7%A4%BA%E5%87%BA%E6%9D%A5%2C%E5%B9%B6%E8%AF%B4%E6%98%8E)
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=3^22^2+(2x3)^2+3^2=49=7^23^2+(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
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.
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=3^22^2+(2x3)^2+3^2=49=7^23^2+(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
(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)
(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+...
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(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+(n+1)^2=2n^2+2n+1;右式-[n(n+1)]^2=(n^2+n+1)^2-(n^2+n)^2=[(n^2+n+1)-(n^2+n)][(n^2+n+1)+(n^2+n)]=2n^2+2n^+1=-[n(n+1)]^2;所以左式=右式.证毕.
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