先观察下列等式,①√1+1/1²+1/2²=1+1/1-1/1+1=1又1/2②√1+1/2²+1/3²=1+1/2-1/1+2=1又1/6(1)根据上面两个等式提供的信息,请猜想√1+1/4²+1/5²的结果并验证(2)按照上面各等式反映
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![先观察下列等式,①√1+1/1²+1/2²=1+1/1-1/1+1=1又1/2②√1+1/2²+1/3²=1+1/2-1/1+2=1又1/6(1)根据上面两个等式提供的信息,请猜想√1+1/4²+1/5²的结果并验证(2)按照上面各等式反映](/uploads/image/z/8601209-17-9.jpg?t=%E5%85%88%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E7%AD%89%E5%BC%8F%2C%E2%91%A0%E2%88%9A1%2B1%2F1%26%23178%3B%2B1%2F2%26%23178%3B%3D1%2B1%2F1-1%2F1%2B1%3D1%E5%8F%881%2F2%E2%91%A1%E2%88%9A1%2B1%2F2%26%23178%3B%2B1%2F3%26%23178%3B%3D1%2B1%2F2-1%2F1%2B2%3D1%E5%8F%881%2F6%EF%BC%881%EF%BC%89%E6%A0%B9%E6%8D%AE%E4%B8%8A%E9%9D%A2%E4%B8%A4%E4%B8%AA%E7%AD%89%E5%BC%8F%E6%8F%90%E4%BE%9B%E7%9A%84%E4%BF%A1%E6%81%AF%2C%E8%AF%B7%E7%8C%9C%E6%83%B3%E2%88%9A1%2B1%2F4%26%23178%3B%2B1%2F5%26%23178%3B%E7%9A%84%E7%BB%93%E6%9E%9C%E5%B9%B6%E9%AA%8C%E8%AF%81%EF%BC%882%EF%BC%89%E6%8C%89%E7%85%A7%E4%B8%8A%E9%9D%A2%E5%90%84%E7%AD%89%E5%BC%8F%E5%8F%8D%E6%98%A0)
先观察下列等式,①√1+1/1²+1/2²=1+1/1-1/1+1=1又1/2②√1+1/2²+1/3²=1+1/2-1/1+2=1又1/6(1)根据上面两个等式提供的信息,请猜想√1+1/4²+1/5²的结果并验证(2)按照上面各等式反映
先观察下列等式,①√1+1/1²+1/2²=1+1/1-1/1+1=1又1/2
②√1+1/2²+1/3²=1+1/2-1/1+2=1又1/6
(1)根据上面两个等式提供的信息,请猜想√1+1/4²+1/5²的结果并验证
(2)按照上面各等式反映的规律,试写出n(n为正整数)表示的等式
先观察下列等式,①√1+1/1²+1/2²=1+1/1-1/1+1=1又1/2②√1+1/2²+1/3²=1+1/2-1/1+2=1又1/6(1)根据上面两个等式提供的信息,请猜想√1+1/4²+1/5²的结果并验证(2)按照上面各等式反映
(1)√(1+1/4²+1/5²) = 1 + 1/4 - 1/(1+4) = 21/20(1又1/20),验证直接计算即可
(2)√[1+1/n²+1/(n+1)²] = 1 + 1/n - 1/(1+n) = (n²+n+1)/(n²+n)(也可写成 1又1/[n*(n+1)] )