\(\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{95.96}\\ =\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{95}-\dfrac{1}{96}\\ =\dfrac{1}{3}-\dfrac{1}{96}\\ =\dfrac{32}{96}-\dfrac{1}{96}\\ =\dfrac{31}{96}\)
\(\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+...+\dfrac{1}{95\cdot96}\)
\(=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}+...+\dfrac{1}{95}+\dfrac{1}{95}-\dfrac{1}{96}\)
\(=\dfrac{1}{3}-\dfrac{1}{96}\)
\(=\dfrac{31}{96}\)
13.4+14.5+...+195.96=13−14+14−15+...+195−196=13−196=3296−196=3196
