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1/（X+1)(X+2）+1/(X+2))(X+3)+...+1/(X+2005)(X+2006)=1/2X+4012
题目详情
1/（X+1)(X+2）+1/(X+2))(X+3)+...+1/(X+2005)(X+2006)=1/2X+4012
▼优质解答
答案和解析
1/（X+1)(X+2）+1/(X+2))(X+3)+...+1/(X+2005)(X+2006)=1/2X+4012
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+2005)-1/(x+2006)=1/2(x+2006)
1/(x+1)-1/(x+2006)=(1/2)*1/(x+2006)
1/(x+1)=(3/2)*1/(x+2006)
3(x+1)=2(x+2006)
x=4012-3
x=4009
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+2005)-1/(x+2006)=1/2(x+2006)
1/(x+1)-1/(x+2006)=(1/2)*1/(x+2006)
1/(x+1)=(3/2)*1/(x+2006)
3(x+1)=2(x+2006)
x=4012-3
x=4009
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