1/3.4+1/4.5+1/5.6+...+1/97.98+1/98.99
=>1/3-1/4+1/4-1/5-........-1/98+1/98-1/99
=>1/3-1/99
=>33/99-1/99=32/99
\(=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{97}-\dfrac{1}{98}+\dfrac{1}{98}-\dfrac{1}{99}\)
\(=\dfrac{1}{3}-\dfrac{1}{99}=\dfrac{33}{99}-\dfrac{1}{99}=\dfrac{32}{99}\)
=1/3 - 1/4 +1/4-1/5 +...+1/98 - 1/99
=1/3-1/99=32/99
\(\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+...+\dfrac{1}{97\cdot98}+\dfrac{1}{98\cdot99}\)
\(=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{97}+\dfrac{1}{97}-\dfrac{1}{98}+\dfrac{1}{98}-\dfrac{1}{99}\)
\(=\dfrac{1}{3}-\dfrac{1}{99}\)
\(=\dfrac{33}{99}-\dfrac{1}{99}\)
\(=\dfrac{32}{99}\)
= 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 ... + 1/97 - 1/98 + 1/98 - 1/99
= 1/3 + ( - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 ... + 1/97 - 1/98 + 1/98 ) - 1/99
= 1/3 + 0 - 1/99
= 1/3 - 1/99
= 32/99
