求1/X(X+3)+1/(X+3)(X+6)+……+1/(X+2007)(X+2010)
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求1/X(X+3)+1/(X+3)(X+6)+……+1/(X+2007)(X+2010)
求1/X(X+3)+1/(X+3)(X+6)+……+1/(X+2007)(X+2010)
求1/X(X+3)+1/(X+3)(X+6)+……+1/(X+2007)(X+2010)
1/x(x+3)
=1/3*3/x(x+3)
=1/3*[(x+3)-x]/x(x+3)
=1/3*[(x+3)/x(x+3)-x/x(x+3)]
=1/3*[1/x-1/(x+3)]
其他的同样这么化简
原式=1/3*[1/x-1/(x+3)]+1/3*[1/(x+3)-1/(x+6)]+……+1/3[1/(x+2007)-1/(x+2010)]
=1/3*[1/x-1/(x+3)+1/(x+3)-1/(x+6)+……+1/(x+2007)-1/(x+2010)]
中间正负抵消
=1/3*[1/x-1/(x+2010)]
=670/[x(x+2010)]
原式=1/3[1/x-1/(x+3)]+1/3[1/(x+3)-1/(x+6)]+1/3[1/(x+6)-1/(x+9)]+...
+[1/(X+2007)-1/(X+2010)]
=1/3[1/x-X+2010]
除了第一项和最后一项 其他都抵消了
1/x(x+3)
=1/3*3/x(x+3)
=1/3*[(x+3)-x]/x(x+3)
=1/3*[(x+3)/x(x+3)-x/x(x+3)]
=1/3*[1/x-1/(x+3)]
原式=1/3*[1/x-1/(x+3)]+1/3*[1/(x+3)-1/(x+6)]+……+1/3[1/(x+2007)-1/(x+2010)]
=1/3*[1/x-1/(x+3)+1/(x+3)-1/(x+6)+……+1/(x+2007)-1/(x+2010)]
=1/3*[1/x-1/(x+2010)]
=670/[x(x+2010)]