作业帮计算：1/X(X+2)+1/(X+2)(X+4)+...+1/(X+28)(X+30)
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/28 23:53:15
计算：1/X(X+2)+1/(X+2)(X+4)+...+1/(X+28)(X+30)
计算：1/X(X+2)+1/(X+2)(X+4)+...+1/(X+28)(X+30)
计算：1/X(X+2)+1/(X+2)(X+4)+...+1/(X+28)(X+30)
1/2*[1/x-1/(x+2)+1/(x+2)-1/(x+4)......+1/(x+28)-1/(x+30)]
=1/2*[1/x-1/(x+30)]
1/X(X+2)+1/(X+2)(X+4)+...+1/(X+28)(X+30)
＝[1/x-1/(x+2)]*(1/2)+[1/(x+2)-1/(x+4)]*(1/2)+...+[1/(x+28)-1/(x+30)]*(1/2)
=(1/2)[1/x-1/(x+30)]
=(1/2)*30/x(x+30)
=15/x(x+30)
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