\(a.11+13+15+...+147\)
\(=\dfrac{\left[\left(147-11\right):2+1\right]\times\left(147+11\right)}{2}\)
\(=\dfrac{69\times158}{2}\)
\(=69\times79=5451\)
\(b.6+8+10+...+1998\)
\(=\dfrac{\left[\left(1998-6\right):2+1\right]\times\left(1998+6\right)}{2}\)
\(=\dfrac{997\times2004}{2}\)
\(=997\times1002=998994\)
\(a.11+13+15+...+147\)
\(=\left(11+149\right)+\left(13+147\right)+\left(15+145\right)+...+\left(81+89\right)+\left(83+87\right)+85\)
\(=160+160+160+...+160+160+85\)
\(=160\text{×}37+85=5920+85=6005\)
\(b.6+8+10+...+1998\)
\(=\left(6+1998\right)+\left(8+1996\right)+\left(10+1994\right)+...+\left(1000+1004\right)+1002\)
\(=2004+2004+2004+...+2004+1002\)
\(=2004\text{×}996+1002=\text{1995984}+1002=\text{1996986}\)
