作业帮求和裂项相消（2²/1*3）+（4²/3*5）+（6²/5*7）+.+[﹙2n﹚²/（2n-1）*（2n+1）]
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![求和裂项相消（2²/1*3）+（4²/3*5）+（6²/5*7）+.+[﹙2n﹚²/（2n-1）*（2n+1）]](/uploads/image/z/7629253-61-3.jpg?t=%E6%B1%82%E5%92%8C%E8%A3%82%E9%A1%B9%E7%9B%B8%E6%B6%88%EF%BC%882%26%23178%3B%2F1%2A3%EF%BC%89%2B%EF%BC%884%26%23178%3B%2F3%2A5%EF%BC%89%2B%EF%BC%886%26%23178%3B%2F5%2A7%EF%BC%89%2B.%2B%5B%EF%B9%992n%EF%B9%9A%26%23178%3B%2F%EF%BC%882n-1%EF%BC%89%2A%EF%BC%882n%2B1%EF%BC%89%5D)
求和裂项相消（2²/1*3）+（4²/3*5）+（6²/5*7）+.+[﹙2n﹚²/（2n-1）*（2n+1）]
求和裂项相消（2²/1*3）+（4²/3*5）+（6²/5*7）+.+[﹙2n﹚²/（2n-1）*（2n+1）]
求和裂项相消（2²/1*3）+（4²/3*5）+（6²/5*7）+.+[﹙2n﹚²/（2n-1）*（2n+1）]
（2²/1*3）+（4²/3*5）+（6²/5*7）+.+[﹙2n﹚²/（2n-1）*（2n+1）]
=n+1/1*3+1/3*5）+1/5*7+.+1/（2n-1）*（2n+1）
=n+[1-1/3+1/3-1/5+1/5-1/7+……+1/(2n-1)-1/(2n+1)]÷2
=n+[1-1/(2n+1)]÷2
=n+2n/(2n+1)÷2
=n+n/(2n+1)
（2²/1*3）+（4²/3*5）+（6²/5*7）+....+[﹙2n﹚²/（2n-1）*（2n+1）]
=n+1/1*3+1/3*5）+1/5*7+....+1/（2n-1）*（2n+1）
=n+[1-1/3+1/3-1/5+1/5-1/7+……+1/(2n-1)-1/(2n+1)]÷2
=n+[1-1/(2n+1)]÷2
=n+2n/(2n+1)÷2
=n+n/(2n+1)