Giải:
M=\(\dfrac{3}{3.5}+\dfrac{3}{5.7}+\dfrac{3}{7.9}+...+\dfrac{3}{95.97}+\dfrac{3}{97.99}\)
M=\(\dfrac{3}{2}.\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{95.97}+\dfrac{2}{97.99}\right)\)
M=\(\dfrac{3}{2}.\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{95}-\dfrac{1}{97}+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
M=\(\dfrac{3}{2}.\left(\dfrac{1}{3}-\dfrac{1}{99}\right)\)
M=\(\dfrac{3}{2}.\dfrac{32}{99}\)
M=\(\dfrac{16}{33}\)
Chúc bạn học tốt!
M= 3/3.5 + 3/5.7 + 3/7.9 +.......+ 3/95.97 + 3/97.99
=3.1/2 ( 2/3.5+...+2/97.99)
=3.1/2(1/3- 1/5+...+1/97+1/99)
=3.1/2(1/3- 1/99)
=(3/2).(32/99)
=96/891
n/xét
3/3.5=(3/3-3/5).1/2
3/5.7=(3/5-3/7).1/2
...
3/97.99=(3/97-3/99).1/2
vậy M=(3/3-3/5).1/2+(3/5-3/7).1/2+...+(3/97-3/99).1/2
⇒M=1/2.(3/3-3/7+3/5-3/7+...+3/97-3/99)
=1/2.(3/3-3/99)
=1/2.32/33
M =16/33
VẬY M=16/33
M= 3/3.5 + 3/5.7 + 3/7.9 +.......+ 3/95.97 + 3/97.99
M=3/2.(2/3.5 +2/5.7 +2/7.9 +...+2/95.97 +2/97.99)
M=3/2.(1/3 -1/5 +1/5-1/7 +1/7-1/9+...+1/95-1/97+1/97-1/99)
M=3/2.(1/3-1/99)
M=3/2.32/99
M=16/33