Question

x+(x+1)+(x+2)+...+(x+2010)=2029099

2+4+6+8+...+2x=210

Answer 1

Ta có : x + (x+1) + (x+2) + ... + (x+2010) = 2029099

=> 2011x + 1 + 2 +... + 2010 = 2029099

=> \(2011x+\frac{2010.2011}{2}=2029099\)

\(\Rightarrow2011x=2029099-2021055=8044\)

=> x = 4

2 + 4 + 6 + 8 +... + 2x = 210

=> 2.1+2.2+2.3+2.4+...+2.x=210

=> 2(1+2+3+...+x) = 210

=> 1 + 2 +3 +...+ x = 105

=> \(\frac{x\left(x+1\right)}{2}=105\Leftrightarrow x\left(x+1\right)=210=14.15\)

=> x = 14