1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)……1/(a+2009)(a+2010)怎么解
问题描述：
1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)……1/(a+2009)(a+2010)怎么解
答
这个数可以是4290,4590,4890
sinA+cosA=根号2
平方
sin2A+cos2A+2sinA*cosA=2
1+2sinA*cosA=2
sinA*cosA=1/2
答
原式=1/a-1/(a+1)+1/(a+1)-1/(a+2)+……+1/(a+2009)-1/(a+2010)
=1/a-1/(a+2010)
=2010/a(a+2010)