a) \(S_1=1+2+3+....+999=\dfrac{\left[\left(999-1\right):1+1\right].\left(999+1\right)}{2}=999.1000:2=999.500=499500\)b) \(S_2=10+12+14+...+2010\dfrac{\left[\left(2010-10\right):2+1\right].\left(2010+10\right)}{2}=1001.2020:2=1001.1010=1011010\)