x/1*2+x/2*3+.+x/2010*2011 = 2010
即1/1*2+1/2*3+.+1/2010*2011 = 2010/x
裂项求和 1/1 - 1/2 + 1/2 -1/3 + …… + 1/2010 - 1/2011 = 2010/x
1 - 1/2011 = 2010/x
2010/2011 = 2010/x
x = 2011