设s1=1+1/1²+1/2²,s2=1+1/2²+1/3²,s3=1+1/3²+1/4²,…Sn=1+1/n²+1/(n+1)²,设√s1√s2+…+√sn,则s= (用含n的代数式表示,其中n为正整数)
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![设s1=1+1/1²+1/2²,s2=1+1/2²+1/3²,s3=1+1/3²+1/4²,…Sn=1+1/n²+1/(n+1)²,设√s1√s2+…+√sn,则s= (用含n的代数式表示,其中n为正整数)](/uploads/image/z/3114498-66-8.jpg?t=%E8%AE%BEs1%3D1%2B1%EF%BC%8F1%26%23178%3B%2B1%EF%BC%8F2%26%23178%3B%2Cs2%3D1%2B1%EF%BC%8F2%26%23178%3B%2B1%EF%BC%8F3%26%23178%3B%2Cs3%3D1%2B1%EF%BC%8F3%26%23178%3B%2B1%EF%BC%8F4%26%23178%3B%2C%E2%80%A6Sn%3D1%2B1%EF%BC%8Fn%26%23178%3B%2B1%EF%BC%8F%28n%2B1%29%26%23178%3B%2C%E8%AE%BE%E2%88%9As1%E2%88%9As2%2B%E2%80%A6%2B%E2%88%9Asn%2C%E5%88%99s%3D++++++++++++++%28%E7%94%A8%E5%90%ABn%E7%9A%84%E4%BB%A3%E6%95%B0%E5%BC%8F%E8%A1%A8%E7%A4%BA%2C%E5%85%B6%E4%B8%ADn%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%29)
设s1=1+1/1²+1/2²,s2=1+1/2²+1/3²,s3=1+1/3²+1/4²,…Sn=1+1/n²+1/(n+1)²,设√s1√s2+…+√sn,则s= (用含n的代数式表示,其中n为正整数)
设s1=1+1/1²+1/2²,s2=1+1/2²+1/3²,s3=1+1/3²+1/4²,…Sn=1+1/n²+1/(n+1)²,设√s1√s2+…+√sn,则s= (用含n的代数式表示,其中n为正整数)
设s1=1+1/1²+1/2²,s2=1+1/2²+1/3²,s3=1+1/3²+1/4²,…Sn=1+1/n²+1/(n+1)²,设√s1√s2+…+√sn,则s= (用含n的代数式表示,其中n为正整数)
∵sn=1+[n^2+(n+1)^2]/[n²(n+1)²]=(n^2+n+1)^2/[n²(n+1)²]
∴√sn=(n^2+n+1)/[n(n+1)]=1+1/n-1/(n+1)
∴s=(1+1-1/2)+(1+1/2-1/3)+(1+1/3-1/4)+……+[1+1/n-1/(n+1)]
=n+(1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1))
=n+(1-1/(n+1))=n+1-1/(n+1)
算出√s1=3/2 √s2=7/6 √s3=13/12
设 n分别等于 1 2 3 …… 则 将√s1=3/2 √s2=7/6 √s3=13/12 …… 分别加起来
分别等于 3/2 8/3 15/4 …… 由此得出 (n2+2n)/(n+1)
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