\(N=\frac{1}{1x5}+\frac{1}{5x10}+...+\frac{1}{2005x2010}\)

\(\Rightarrow5N=\frac{5}{1x5}+\frac{5}{5x10}+\frac{5}{10x15}+...+\frac{5}{2005x2010}\)

\(\Rightarrow5N=1-\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+...+\frac{1}{2005}-\frac{1}{2010}\)

\(\Rightarrow5N=1-\frac{1}{5}-\frac{1}{2010}\)

\(\Rightarrow5N=\frac{4}{5}-\frac{1}{2010}\)

\(\Rightarrow5N=\frac{1607}{2010}\)

\(\Rightarrow N=\frac{1607}{10050}\)

Nhấn đúng cho mk nha!!!!!!!!!

\(=\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+..........+\frac{1}{2005}-\frac{1}{2010}\)

\(=\frac{1}{1}-\frac{1}{2010}\)

\(=\frac{2009}{2010}\)

\(N=\frac{1}{1.5}+\frac{1}{5.10}+...+\frac{1}{2005.2010}=\frac{1}{5}\left(\frac{5}{1.5}+\frac{5}{5.10}+...+\frac{5}{2005.2010}\right)=\frac{1}{5}\left(\frac{1}{1}-\frac{1}{5}+...+\frac{1}{2005}-\frac{1}{2010}\right)\)

\(N=\frac{1}{5}.\frac{2009}{2010}=\frac{2009}{2010}\)

Bài bạn Mạnh Chưa đúng. bạn  Hạnh kiểm tra lại nhé

\(N=\frac{1}{1.5}+\frac{1}{5.10}+....+\frac{1}{2005.2010}\)

\(N=5.\left(\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+....+\frac{1}{2005}-\frac{1}{2010}\right)\)

\(N=5.\left(\frac{1}{1}-\frac{1}{2010}\right)\)

\(N=5.\frac{2009}{2010}\)

\(N=\frac{2009}{402}\)

N = 1/1x5 + 1/5x10 + 1/10x15 + 1/15x20 + .....+1/2005 x 2010

N = 1 - 1/5 +1/5-1/5+1/10-1/15+1/5-1/20+.....+1/2005-1/2010

N = 1 - 1/2010

N = 2009/2010

Ta có:

\(N=\frac{1}{1x5}+\frac{1}{5x10}+\frac{1}{10x15}...+\frac{1}{2005x2010}\)

\(\Rightarrow Nx5=\left(\frac{1}{1x5}+\frac{1}{5x10}+\frac{1}{10x15}...+\frac{1}{2005x2010}\right)x5\)

\(=\frac{5}{1x5}+\frac{5}{5x10}+\frac{5}{10x15}...+\frac{5}{2005x2010}\)

\(=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+...+\frac{1}{2005}-\frac{1}{2010}\)

\(=1-\frac{1}{2010}\)

\(=\frac{2009}{2010}\)

\(\Rightarrow N=\frac{2009}{2010}:5=\frac{2009}{2010}x\frac{1}{5}=\frac{2009}{10050}\)

Bạn thuỳ dung ơi cho hỏi sao 5/(1x5) = 1 - 1/5 vậy ???

Đặt A = 1/5x10 + 1/10x15 + 1/15x20 + 1/20x25 + ... + 1/95x100

A x 5 = 5/5x10 + 5/10x15 + 5/15x20 + 5/20x25 + ... + 5/95x100

A x 5 = 1/5 - 1/10 + 1/10 - 1/15 + 1/15 - 1/20 + 1/20 - 1/25 + ... + 1/95 - 1/100

A x 5 = 1/5 - 1/100

A x 5 = 19/100

A = 19/100 : 5

A = 19/100 x 1/5 

A = 19/500

 Vậy A= 19/500

chỉ cần phân k nha bạn 

kết bạn vs mình nói cho

các bạn tíck cho mình thì sẽ trả cho 3 tíck

Ta có :

\(\frac{1}{2009}+\frac{2}{2009}+....+\frac{2008}{2009}\)

\(=\frac{1+2+....+2008}{2009}\)

\(=\frac{2017036}{2009}=1004\)

Ta có ; \(\frac{1}{2009}+\frac{2}{2009}+\frac{3}{2009}+......+\frac{2008}{2009}\)

\(=\frac{1+2+3+......+2008}{2009}\)

\(=\frac{2017036}{2009}=1004\)

Ta có :

\(\frac{1}{2009}+\frac{2}{2009}+......+\frac{2008}{2009}\)

 \(=\frac{1+2+3+....+2008}{2009}\)

\(=\frac{2017036}{2009}=1004\)

gọi biểu thức là A

A=1/2+1/4+1/8+...+1/2048=1/2+1/2^2+1/2^3+...+1/2^10

=>2A=1+1/2+1/2^2+...+1/2^9

=>A=2A-A(bạn đặt cột dọc ra rồi sẽ thấy:1/2-1/2=0;1/2^2-1/2^2=0;...)Ta được kết quả bằng 1+1/2^10

Đặt A =1/2 + 1/4 + 1/8 + ...+ 1/1024 + 1/2048

A= 1/2 + 1/2^2 + 1/2^3+...+ 1/2^10 + 1/2^11

2A= 1 +1/2 + 1/2^2 +...+ 1/2^9 + 1/2^10

2A-A= (1 +1/2 + 1/2^2 +...+ 1/2^9 + 1/2^10) - (1/2 + 1/2^2 + 1/2^3+...+ 1/2^10 + 1/2^11)

A= 1+1/2 + 1/2^2 +...+ 1/2^9 + 1/2^10 - 1/2 - 1/2^2 - 1/2^3 - ...- 1/2^10 - 1/2^11

A= 1- 1/2^11

A= 2047/ 2048

Đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+...+\frac{1}{1024}+\frac{1}{2048}\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+...+\frac{1}{512}+\frac{1}{1024}\)
\(2A-A=1-\frac{1}{2048}\)
\(A=\frac{2047}{2048}\)

\(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)

\(A=\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+\frac{1}{11\cdot12}\)

\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)

\(A=\frac{1}{5}-\frac{1}{12}=\frac{7}{60}\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(=1-\left(\frac{1}{2}-\frac{1}{2}\right)-\left(\frac{1}{3}-\frac{1}{3}\right)-......-\left(\frac{1}{6}-\frac{1}{6}\right)-\frac{1}{7}\)

\(=1-\frac{1}{7}\)

\(=\frac{6}{7}\)

1/2+1/6+1/12+1/20+1/30+1/42

=1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7

=1-1/7

=6/7

nhớ tách ra rồi mới cộng với trừ nhé!