Lời giải:

Đặt biểu thức trên là $A$.
\(2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+....+\frac{2}{37.38.39}\)

\(=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{39-37}{37.38.39}\)

\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{37.38}-\frac{1}{38.39}\)

\(=\frac{1}{1.2}-\frac{1}{38.39}=\frac{370}{741}\)

\(\Rightarrow A=\frac{185}{741}\)

= 1 . 1/2 . 1/3 + 1/2 . 1/3 . 1/4 + ... + 1/37 . 1/38 . 1/39

= 1 . 1/39

= 1/39

Mong moi nguoi chi them03

thank you nhe

x =1/20+1/40+1/88+1/154=5/21

1/1.2.3+1/2.3.4+1/3.4.5+...+1/37.38.39

= 1/2.(1/1.2-1/2.3)+1/2.(1/2.3-1/3.4)+...+1/2.(1/37.38-1/38.39)

= 1/2.(1/1.2-1/2.3+1/2.3-1/3.4+...+1/37.38-1/38.39)

= 1/2.(1/1.2-1/38.39)

= 1/2.370/741

= 185/741

Ta có 
1/(1.2.3) = 1/2.(1/(1.2) - 1/(2.3)) 
1/(2.3.4) = 1/2.(1/(2.3) - 1/(3.4)) 
1/(3.4.5) = 1/2.(1/(3.4) - 1/(4.5)) 
......... 
......... 
1/( 37.38.39) = 1/2.((1/(37.38) - 1/(38.39)) 
Cộng vế với vế các đẳng thức trên ta được. 
1/( 1.2.3) + 1/ ( 2.3.4) + 1/(3.4.5) +...........+ 1/( 37.38.39) = 1/2.( 1/(1.2) - 1/(2.3) + 1/(2.3) - 1/(3.4) + 1/(3.4) - 1/(4.5) + ......1/(37.38) - 1/(38.39) 
=> 1/( 1.2.3) + 1/ ( 2.3.4) + 1/(3.4.5) +...........+ 1/( 37.38.39) = 1/2.( 1/(1.2) - 1/(38.39)) = 185/74 

                                    Đ/S:tích

bằng \(\frac{185}{741}\)mà bạn!!

Ta có 
1/(1.2.3) = 1/2.(1/(1.2) - 1/(2.3)) 
1/(2.3.4) = 1/2.(1/(2.3) - 1/(3.4)) 
1/(3.4.5) = 1/2.(1/(3.4) - 1/(4.5)) 
......... 
......... 
1/( 37.38.39) = 1/2.((1/(37.38) - 1/(38.39)) 
Cộng vế với vế các đẳng thức trên ta được. 
1/( 1.2.3) + 1/ ( 2.3.4) + 1/(3.4.5) +...........+ 1/( 37.38.39) = 1/2.( 1/(1.2) - 1/(2.3) + 1/(2.3) - 1/(3.4) + 1/(3.4) - 1/(4.5) + ......1/(37.38) - 1/(38.39) 
=> 1/( 1.2.3) + 1/ ( 2.3.4) + 1/(3.4.5) +...........+ 1/( 37.38.39) = 1/2.( 1/(1.2) - 1/(38.39)) = 185/74 

dang tuan anh kết quả là 185/74 không

1-1/3+1/3-1/5+1/5-1/7+.......+1/37-1/39

1-1/39

38/39

Lời giải:
\(2A=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+....+\frac{38-36}{36.37.38}+.\frac{39-37}{37.38.39}\)

\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{36.37}-\frac{1}{37.38}+\frac{1}{37.38}-\frac{1}{38.39}\)

\(=\frac{1}{1.2}-\frac{1}{38.39}=\frac{370}{741}\)

D = \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{37.38.39}\)

D = \(\frac{1}{2}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+...+\frac{39-37}{37.38.39}\right)\)

D = \(\frac{1}{2}.\left(\frac{3}{1.2.3}-\frac{1}{1.2.3}+\frac{4}{2.3.4}-\frac{2}{2.3.4}+...+\frac{39}{37.38.39}-\frac{37}{37.38.39}\right)\)

D = \(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{37.38}-\frac{1}{38.39}\right)\)

D = \(\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{38.39}\right)\)

D = \(\frac{1}{2}.\frac{370}{741}\)

D = \(\frac{185}{741}\)

\(A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{37.38.39}\)

\(A=\dfrac{1}{2}\left(\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+...+\dfrac{2}{37.38.39}\right)\)

\(A=\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{37.38}-\dfrac{1}{38.39}\right)\)

\(A=\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{38.39}\right)\)

\(A=\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{1482}\right)\)

\(A=\dfrac{1}{2}.\dfrac{370}{741}=\dfrac{185}{741}\)