Question

解方程：x/1*2+x/2*3+x/3*4+.+x/2005*2006=2005

Answer 1

x/1*2 + x/2*3 + x/3*4 + ... + x/2005*2006 = 2005

x(1 - 1/2) + x(1/2 - 1/3) + x(1/3 - 1/4) + ... + x(1/2005 - 1/2006) = 2005

x(1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2005 - 1/2006) = 2005

x (1 - 1/2006) = 2005

2005x/2006 = 2005

x = 2006