\(\dfrac{4}{1.3}+\dfrac{4}{3.5}+\dfrac{3}{5.7}+...+\dfrac{4}{97.99}\)
\(=2\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{97.99}\right)\)
\(=2\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(=2\left(1-\dfrac{1}{99}\right)\)
\(=2\cdot\dfrac{98}{99}\)
\(=\dfrac{196}{99}\)
#NoSimp
=2(2/1*3+2/3*5+...+2/97*99)
=2(1-1/3+1/3-1/5+...+1/97-1/99)
=2*98/99=196/99
\(\dfrac{4}{1.3}+\dfrac{4}{3.5}+\dfrac{4}{5.7}+...+\dfrac{4}{97.99}\)
=4.(\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{97.99}\)
=4.1/2.(2/1.3+2/3.5+2/5.7+...+2/97.99)
=2.(1/1-1/3+1/3-1/5+1/5-1/7+...+1/97-1/99)
=2.(1/1-1/99)
=2.(99/99-1/99)
=2.98/99
=196/99