Áp dụng công thức \(\frac{2}{a\left(a+1\right)\left(a+2\right)}=\frac{1}{a\left(a+1\right)}-\frac{1}{\left(a+1\right)\left(a+2\right)}\), ta có:

\(\frac{2}{1.2.3}=\frac{1}{1.2}-\frac{1}{2.3}\)

\(\frac{2}{2.3.4}=\frac{1}{2.3}-\frac{1}{3.4}\)

.........

\(\frac{2}{37.38.39}=\frac{1}{37.38}-\frac{1}{38.39}\)

Cộng các vế lại ta được:

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

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

em tịt lun

Câu hỏi của Hoàng Như Anh ngày 1/07/2015

k mk nha

5,Ta có

A=1/2+1/2^2+1/2^3+...+1/2^100

2A=1+1/2+1/2^2+1^2/3+...+1/2^99

2A-A=(1+1/2+1/2^2+1^2/3+...+1/2^99)-(1/2+1/2^2+1/2^3+...+1/2^100)

A=1-1/2^100

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

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

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

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

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

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

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

=1/1-1/39

=39/39-1/39 =38/39

Làm đại ko biết đúng hay sai hên xui nha=v='

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

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

A=1/2.370/741

A=185/741

A = \(\frac{2}{1.2.3}+\frac{2}{2.3.4}+....+\frac{2}{37.38.39}\)

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

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

A = \(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{37.18}-\frac{1}{38.39}\)

A = \(\frac{1}{2}-\frac{1}{38.39}\)

A = \(\frac{370}{741}\)

21320

Em nói thật em mới học lớp 6 Màu em đã phải làm bài này rồi thật đấu không phải đùa đâu

Ta có: 2/1.2.3=1/1.2-1/3.4

2/2.3.4=1/2.3-1/3.4

2/3.4.5=1/3.4-1/4.5

2/37.38.39=1/37.38-1/38.39

=>2A=1/1.2-1/2.3+1/2.3-1/3.4+1/3.4-1/4.5+......+1/37.38-1/38.39

= 1/1.2-1/38.39=370/741

​=> A= 370/741

C = \(2\cdot\left(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{37\cdot38\cdot39}\right)\)

=> C = \(2\cdot\left(\left(1-\frac{1}{2}-\frac{1}{3}\right)+...+\left(\frac{1}{37}-\frac{1}{38}-\frac{1}{39}\right)\right)\)

=> C = \(2\cdot\left(1-\frac{1}{39}\right)=2\cdot\frac{38}{39}=\frac{76}{39}\)