一道初二下学期分式的加减计算计算:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+…+1/(x+1998)(x+1999),并求当x=1时,该代数式的值.希望能详细一点,愿意帮我解说一下,我会加分的,但是也不要
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![一道初二下学期分式的加减计算计算:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+…+1/(x+1998)(x+1999),并求当x=1时,该代数式的值.希望能详细一点,愿意帮我解说一下,我会加分的,但是也不要](/uploads/image/z/8785624-40-4.jpg?t=%E4%B8%80%E9%81%93%E5%88%9D%E4%BA%8C%E4%B8%8B%E5%AD%A6%E6%9C%9F%E5%88%86%E5%BC%8F%E7%9A%84%E5%8A%A0%E5%87%8F%E8%AE%A1%E7%AE%97%E8%AE%A1%E7%AE%97%EF%BC%9A1%2Fx%EF%BC%88x%2B1%EF%BC%89%2B1%2F%EF%BC%88x%2B1%EF%BC%89%EF%BC%88x%2B2%EF%BC%89%2B1%2F%EF%BC%88x%2B2%EF%BC%89%EF%BC%88x%2B3%EF%BC%89%2B%E2%80%A6%2B1%2F%EF%BC%88x%2B1998%EF%BC%89%EF%BC%88x%2B1999%EF%BC%89%2C%E5%B9%B6%E6%B1%82%E5%BD%93x%3D1%E6%97%B6%2C%E8%AF%A5%E4%BB%A3%E6%95%B0%E5%BC%8F%E7%9A%84%E5%80%BC.%E5%B8%8C%E6%9C%9B%E8%83%BD%E8%AF%A6%E7%BB%86%E4%B8%80%E7%82%B9%2C%E6%84%BF%E6%84%8F%E5%B8%AE%E6%88%91%E8%A7%A3%E8%AF%B4%E4%B8%80%E4%B8%8B%2C%E6%88%91%E4%BC%9A%E5%8A%A0%E5%88%86%E7%9A%84%2C%E4%BD%86%E6%98%AF%E4%B9%9F%E4%B8%8D%E8%A6%81)
一道初二下学期分式的加减计算计算:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+…+1/(x+1998)(x+1999),并求当x=1时,该代数式的值.希望能详细一点,愿意帮我解说一下,我会加分的,但是也不要
一道初二下学期分式的加减计算
计算:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+…+1/(x+1998)(x+1999),并求当x=1时,该代数式的值.
希望能详细一点,愿意帮我解说一下,我会加分的,但是也不要太乱了,
一道初二下学期分式的加减计算计算:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+…+1/(x+1998)(x+1999),并求当x=1时,该代数式的值.希望能详细一点,愿意帮我解说一下,我会加分的,但是也不要
1/x(x+1)=1/x-1/(x+1)
1/(x+1)(x+2)=1/(x+1)-1/(x+2)
1/(x+2)(x+3)=1/(x+2)-1/(x+3)
……
1/(x+1998)(x+1999)=1/(x+1998)-1/(x+1999)
所以,
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+1998)(x+1999)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+
1/(x+1998)-1/(x+1999)
=1/x-1/(x+1999)
当x=1时,
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+1998)(x+1999)
=1/x-1/(x+1999)
=1-1/2000
=1999/2000