\(2+4+6+...+2x=1010\)\(0\)
\(\Rightarrow2.\left(1+2+3+...+x\right)=10100\)
\(\Rightarrow1+2+3+...+n=10100:2=5050\)
\(\Rightarrow n.\left(n+1\right):2=5050\)
\(\Rightarrow n.\left(n+1\right)=5050.2=10100\)
\(\Rightarrow n.\left(n+1\right)=100.101\)
\(\Rightarrow n=100\)
\(2+4+6+.......+2x=10100.\)
\(2\cdot1+2\cdot2+2\cdot3+........+2x=10100\)
\(2\cdot\left(1+2+3+.....+x\right)=10100\)
\(1+2+3+....+x=10100:2\)
\(1+2+3+...+x=5050\)
\(\Rightarrow\left(x+1\right).\left(x-1+1\right):2=5050\)
\(\left(x+1\right).x:2=5050\)
\(\Rightarrow x.\left(x+1\right)=5050.2=10100\)
\(\text{Mà:}10100=2^2\cdot5^2\cdot101=100\cdot101\)
\(\Rightarrow x=100\)
