\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2008}{2010}\)
\(\Leftrightarrow2\left(\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{\left(x+1\right)-x}{x\left(x+1\right)}\right)=\frac{2008}{2010}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2008}{2010}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{1004}{2010}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2010}\)
\(\Leftrightarrow x+1=2010\)
\(\Leftrightarrow x=2009\)

qua de dang nhe

S=1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+4+...+10)

S=1/(2*3/2)+1/(3*4/2)+1/(4*5/2)+...+1/(10*11/2)

S=2(1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+...+1/(10*11)

S=2(1/2-1/3+1/3-1/4+1/4-1/5+...+1/10-1/11)

S=2(1/2-1/11)

S=2*9/22

S=9/11

nho k cho minh voi nha

\(S=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+10}\)

\(S=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{55}\)

\(S=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{110}\)

\(S=2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}\right)\)

\(S=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}\right)\)

\(S=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\right)\)

\(S=2\left(\frac{1}{2}-\frac{1}{11}\right)\)

\(S=2.\frac{9}{22}\)

\(S=\frac{9}{11}\)

a) = 2(1-1/2+1/2-1/3+...+1/19-1/20)

    = 2(1-1/20)

    = 2.19/20

    = 19/10

b) = 7(1/2-1/3+1/3-1/4+...+1/6-1/7)

   = 7(1/2 - 1/7)

   = 7.5/14

   = 5/2

c) = 1/2-1/5+1/5-1/8+...+1/14-1/17

   = 1/2 - 1/17

   = 15/34

Chúc bạn học tốt nhé

a)2/1.2+2/2.3+....+2/19.20

=2(1/1.2+1/2.3+....+1/19.20)

=2(1-1/2+1/2-1/3+.....-1/20)

=2(1-1/20)

2(19/20)=38/20=19/10

b)7/2.3+7/3.4+7/4.5+7/5.6+7/6.7

7(1/2.3+1/3.4+1/4.5+1/5.6+1/6.7)

7(1/2-1/3+1/3-1/4+.....-1/7)

7(1/2-1/7)

7(7/14-2/14)=7.5/14=35/14=5/2

c)3/2.5+3/5.8+3/8.11+3/11.14+3/14.17

1/2-1/5+1/5-1/8+......+1/14-1/17

1/2-1/17=17/34-2/34=15/34

Đây là toán lp 6 chứ bn

A = 2/1.2 + 2/2.3 + ...+2/19.20

Áp dụng công thức : n/n.(n+1)=(1/n)-(1/n+1)

Ta có : A= 1/1.2 + 1/2.3+...+1/19.20

           A= 1/1 - 1/2 + 1/2 - 1/3 + ...+ 1/19 - 1/20

           A= 1/1 - 1/20 

           A= 19/20

k cho mk nha bn

\(\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\frac{2}{4\cdot5}+...+\frac{2}{99\cdot100}\)

\(=2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{99\cdot100}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=2\cdot\frac{49}{100}\)

\(=\frac{49}{50}\)

=2(\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+\(\frac{1}{4.5}\)+...+\(\frac{1}{99.100}\))

=2(\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+...+\(\frac{1}{99}\)-\(\frac{1}{100}\))

=2(\(\frac{1}{2}\)-\(\frac{1}{100}\))

=2.\(\frac{49}{100}\)

=\(\frac{49}{50}\)

\(M=\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.\frac{4^2}{4.5}=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}=\frac{1}{5}\)

\(N=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{99.101}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\)

\(=\frac{1}{3}-\frac{1}{101}=\frac{98}{303}\)

N=1/2x(1/3-1/5+1/5-1/7+....+1/99-1/101)

N=1/2x(1/3-1/101)

N=1/2x98/101

N=49/101

nhầm 98/303 mới đúng

\(A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{49.50}\)

\(A=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{49.50}\right)\)

\(A=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\right)\)

\(A=2.\left(\frac{1}{2}-\frac{1}{50}\right)\)

\(A=2.\frac{12}{25}=\frac{2.12}{25}=\frac{24}{25}\)

cảm ơn bạn . kb với mik nha

\(A=\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{49.50}\)

\(\Rightarrow\frac{1}{2}A=\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{98.100}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{4}-\frac{1}{100}\)

\(\Rightarrow\frac{1}{2}A=\frac{6}{25}\)

\(\Rightarrow A=\frac{6}{25}:\frac{1}{2}=\frac{12}{25}\)

2A=2/2.2.3+2/2.3.4+...+2/2.49.50

2A=1/2.3+1/3.4+...+1/49.50

2A=1/2-1/3+1/3-1/4+....+1/49-1/50

2A=1/2-1/50

2A=12/25

A=12/25:2

A=6/25

Mk` tính nhẩm nên chưa chắc đã đúg. Bạn tính lại xem đúg ko nha!

Chúc pn họk tốt!!!!

Sorry. Mk` bị nhầm. Phải làk nhân 1/2 cơ

\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.....\frac{10^2}{10.11}\)

\(=\frac{1.1}{1.2}.\frac{2.2}{2.3}.\frac{3.3}{3.4}......\frac{10.10}{10.11}\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{10}{11}\)

\(=\frac{1.2.3.....10}{2.3.4.....11}=\frac{1}{11}\)