Correct Answer - A
`underset(xrarroo)(lim)(sum_(r=1)^(10)(x+r)^(2010))/((x^(1006)+1)(2x^(1004)+1))`
`" =underset(xrarroo)(lim)((x+1)^(2010)+(x+2)^(2010)+...+(x+10)^(2010))/((x^(1006)+1)(2x^(1004)+1))`
`" "=underset(xrarroo)(lim)((1+(1)/(x))^(2010)+(1+(2)/(x))^(2010)+....+(1+(10)/(x))^(2010))/((1+(1)/(x^(1006)))(2+(1)/(x^(1004))))`
`=(10)/(2)=5`
