\(\text{a=1.2+2.3+3.4+......+98.99}\)
\(=1\left(1\text{+}1\right)\text{+}2\left(2\text{+}1\right)\text{+}3\left(3\text{+}1\right)\text{+}.........\text{+}98\left(98\text{+}1\right)\)
\(=1^2\text{+}1\text{+}1^2\text{+}2\text{+}3^2\text{+}3\text{+}...\text{+}98^2\text{+}98\)
\(=b\text{+}\left(1\text{+}2\text{+}3\text{+}...\text{+}98\right)\)
\(=b\text{+}\left(98\text{+}1\right).98:2\)
\(=b\text{+}4851\)
\(\Rightarrow a-b=4851\)
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