观察下列等式1/1×2=1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4,将以上三等式两边分别相加得1/1×2+1/2×3+1/3×4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4(1)猜想并写出1/n(n+1)= (2)直接写出下列各式的计算结婚:(1)1/1×2+1
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![观察下列等式1/1×2=1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4,将以上三等式两边分别相加得1/1×2+1/2×3+1/3×4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4(1)猜想并写出1/n(n+1)= (2)直接写出下列各式的计算结婚:(1)1/1×2+1](/uploads/image/z/10343738-2-8.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E7%AD%89%E5%BC%8F1%2F1%C3%972%3D1-1%2F2%2C1%2F2%C3%973%3D1%2F2-1%2F3%2C1%2F3%C3%974%3D1%2F3-1%2F4%2C%E5%B0%86%E4%BB%A5%E4%B8%8A%E4%B8%89%E7%AD%89%E5%BC%8F%E4%B8%A4%E8%BE%B9%E5%88%86%E5%88%AB%E7%9B%B8%E5%8A%A0%E5%BE%971%2F1%C3%972%2B1%2F2%C3%973%2B1%2F3%C3%974%3D1-1%2F2%2B1%2F2-1%2F3%2B1%2F3-1%2F4%3D1-1%2F4%3D3%2F4%EF%BC%881%EF%BC%89%E7%8C%9C%E6%83%B3%E5%B9%B6%E5%86%99%E5%87%BA1%2Fn%EF%BC%88n%2B1%EF%BC%89%3D+%EF%BC%882%EF%BC%89%E7%9B%B4%E6%8E%A5%E5%86%99%E5%87%BA%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E8%AE%A1%E7%AE%97%E7%BB%93%E5%A9%9A%3A%EF%BC%881%EF%BC%891%2F1%C3%972%2B1)
观察下列等式1/1×2=1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4,将以上三等式两边分别相加得1/1×2+1/2×3+1/3×4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4(1)猜想并写出1/n(n+1)= (2)直接写出下列各式的计算结婚:(1)1/1×2+1
观察下列等式1/1×2=1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4,将以上三等式两边分别相加得1/1×2+1/2×3+1/3×4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4(1)猜想并写出1/n(n+1)= (2)直接写出下列各式的计算结婚:(1)1/1×2+1/2×3+1/3×4+...+1/2009×2010= (2)1/1×2+1/2×3+1/3×4+...+1/n(n-1)= (3)探究并计算1/2×4+1/4×6+1/6×8+...+1/2008×2010
观察下列等式1/1×2=1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4,将以上三等式两边分别相加得1/1×2+1/2×3+1/3×4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4(1)猜想并写出1/n(n+1)= (2)直接写出下列各式的计算结婚:(1)1/1×2+1
小学数学,裂项相消.
题中有个地方有错:(2)1/1×2+1/2×3+1/3×4+...+1/n(n-1)= 如果用省略号,默认数列满足通式,显然你这儿n-1小于n,格式不对,给你改成(2)1/1×2+1/2×3+1/3×4+...+1/[(n-1)n]计算的
(1) 1/[n(n+1)]= 1/n-1/(n+1)
(2) 1/1×2+1/2×3+1/3×4+...+1/2009×2010=1-1/2010=2009/2010
1/1×2+1/2×3+1/3×4+...+1/[(n-1)n]=1-1/n=(n-1)/n
1/2×4+1/4×6+1/6×8+...+1/2008×2010=1/2*(1/2-1/2010)=1004/2010=502/1005
不知道是不是你想要的结果.