-1/2,2/3,-3/4,4/5,-5/6,7/8 ...猜想第n个数与第n加1个数的和(n是奇数) 有易懂的办法表示一下.
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![-1/2,2/3,-3/4,4/5,-5/6,7/8 ...猜想第n个数与第n加1个数的和(n是奇数) 有易懂的办法表示一下.](/uploads/image/z/3679405-61-5.jpg?t=-1%2F2%2C2%2F3%2C-3%2F4%2C4%2F5%2C-5%2F6%2C7%2F8+...%E7%8C%9C%E6%83%B3%E7%AC%ACn%E4%B8%AA%E6%95%B0%E4%B8%8E%E7%AC%ACn%E5%8A%A01%E4%B8%AA%E6%95%B0%E7%9A%84%E5%92%8C%EF%BC%88n%E6%98%AF%E5%A5%87%E6%95%B0%EF%BC%89+%E6%9C%89%E6%98%93%E6%87%82%E7%9A%84%E5%8A%9E%E6%B3%95%E8%A1%A8%E7%A4%BA%E4%B8%80%E4%B8%8B.)
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-1/2,2/3,-3/4,4/5,-5/6,7/8 ...猜想第n个数与第n加1个数的和(n是奇数) 有易懂的办法表示一下.
-1/2,2/3,-3/4,4/5,-5/6,7/8 ...猜想第n个数与第n加1个数的和(n是奇数) 有易懂的办法表示一下.
-1/2,2/3,-3/4,4/5,-5/6,7/8 ...猜想第n个数与第n加1个数的和(n是奇数) 有易懂的办法表示一下.
数列排列规律:分子为项数,分母为项数+1,奇数项为负,偶数项为正.
n为奇数,第n个数与第n+1个数之和=-n/(n+1) +(n+1)/(n+2)
=[-n(n+2)+(n+1)²]/[(n+1)(n+2)]
=(-n²-2n+n²+2n+1)/[(n+1)(n+2)]
=1/[(n+1)(n+2)]
=1/(n+1) - 1/(n+2)
看