Đáp án:
a)2003/2005
b)4949/9900
Giải thích các bước giải:
a)M=1/3+1/6+1/10+1/15+....+1/2004.2005
M.1/2=1/6+1/12+1/20+1/30+....+1/2004.2005
M.1/2=1/2.3=1/3.4+1/4.5+1/5.6+....+1/2004.2005
M.1/2=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+....+1/2004-1/2005
M.1/2=1/2-1/2005
M.1/2=2003/4010
=>M=2003/2005
b)S=1/1.2.3+1/2.3.4+1/3.4.5+....+1/98.99.100
=2S=2x(1/1.2.3+1/2.3.4+1/3.4.5+...+1/98.99.100)
=2/1.2.3-2/2.3.4-2/3.4.5+....+2/98.99.100
=1/1.2-1/2.3+1/2.3-1/3.4+....+1/98.99-1/99.100
=1/1.2-1/99.100
=4950/9900-1/9900
=4949/9900
