Question

$\frac{x+1}{2} + \frac{x+2}{3} + \frac{x+3}{4} + ... + \frac{x+2010}{2011} - 2010 = 0$
VA ROG!

Answer 1

1/2*x+1/2+1*3*x+2/3+...+1/2011*x+2010/2011=2010
x(1/2+1/3+1/4+...+1/2011)=1-1/2+1-2/3+....+1-2010/2011
x(1/2+1/3+1/4+...+1/2011)=1/2+1/3+1/4+...+1/2011
x=1