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Đặt A = 1/2 - 1/3 - 2/3 + 1/4 + 2/4 + 3/4 - 1/5 - 2/5 - 3/5 - 4/5 + ... + 1/10 + ...+ 9/10

A = 1/2 - ( 1/3 + 2/3) + (1/4 + 2/4 + 3/4) - ( 1/5 + 2/5 + 3/5 + 4/5) + ( 1/6 + 2/6 + ...  + 5/6) - ( 1/7 + 2/7 + ... + 6/7) + ( 1/8 + 2/8 + ... + 7/8) - ( 1/9 + 2/9 + ... + 8/9)

A = 1/2 - 1 + [( 1/4 + 3/4) + 2/4] - [(1/5 + 4/5) + (2/5 + 3/5)] + [(1/6+5/6) + ( 2/6 + 4/6) + 3/6] - [(1/7 + 6/7) + (2/7 + 5/7) + (3/7 + 4/7)] + [(1/8 + 7/8) + (2/8 + 6/8) + (3/8 + 5/8) + 4/8)] - [(1/9 + 8/9) + (2/9 + 7/9) + (3/9 + 6/9) + (4/9 + 5/9)] + [(1/10 + 9/10) + ( 2/10 + 8/10) + ( 3/10 + 7/10) + ( 4/10 + 6/10) + 5/10]

A = 1/2 - 1 + ( 1 + 1/2) - 2 + ( 2 + 1/2) - 3 + ( 3 + 1/2) - 4 + ( 4 + 1/2) 

A = 1/2 + 1/2 + 1/2 + 1/2 + 1/2 

A = 1/2 × 5 = 5/2

Đặt A = 1/2 - 1/3 - 2/3 + 1/4 + 2/4 + 3/4 - 1/5 - 2/5 - 3/5 - 4/5 + ... + 1/10 + ...+ 9/10

A = 1/2 - ( 1/3 + 2/3) + (1/4 + 2/4 + 3/4) - ( 1/5 + 2/5 + 3/5 + 4/5) + ( 1/6 + 2/6 + ...  + 5/6) - ( 1/7 + 2/7 + ... + 6/7) + ( 1/8 + 2/8 + ... + 7/8) - ( 1/9 + 2/9 + ... + 8/9)

A = 1/2 - 1 + [( 1/4 + 3/4) + 2/4] - [(1/5 + 4/5) + (2/5 + 3/5)] + [(1/6+5/6) + ( 2/6 + 4/6) + 3/6] - [(1/7 + 6/7) + (2/7 + 5/7) + (3/7 + 4/7)] + [(1/8 + 7/8) + (2/8 + 6/8) + (3/8 + 5/8) + 4/8)] - [(1/9 + 8/9) + (2/9 + 7/9) + (3/9 + 6/9) + (4/9 + 5/9)] + [(1/10 + 9/10) + ( 2/10 + 8/10) + ( 3/10 + 7/10) + ( 4/10 + 6/10) + 5/10]

A = 1/2 - 1 + ( 1 + 1/2) - 2 + ( 2 + 1/2) - 3 + ( 3 + 1/2) - 4 + ( 4 + 1/2) 

A = 1/2 + 1/2 + 1/2 + 1/2 + 1/2 

A = 1/2 × 5 = 5/2

Ta có : 

\(S=\frac{3}{2}+\frac{4}{3}+\frac{5}{4}+\frac{6}{5}+\frac{7}{6}+\frac{8}{7}+\frac{9}{8}+\frac{10}{9}+\frac{11}{10}+\frac{12}{11}\)

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

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

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

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

\(\Rightarrow\)\(S>10\) 

Vậy \(S>10\)

Chúc bạn học tốt ~ 

1/2+2/3+3/4+4/5+5/6+6/7+7/8+8/9+9/10x9/10

=9/10x(1/2+2/3)+(3/4+4/5)+(5/6+6/7)+(7/8+8/9)

=9/10x(1/3+3/5+5/7+7/9)

9/10x(1/3+3/5)+(5/7+7/9)

=9/10x1/5+5/9

9/50+5/9

=10

Bn Long làm đúng rồi bn   nguyễn kim arica cứ làm theo cách đó là được .

Bn nào thấy đúng thì ủng hộ nha .

hình như đề bạn sai thì phải đúng ko biết ngỏ bạn làm

cái chỗ có 2 phân số 9/10 đấy

\(S=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}.\frac{6}{7}.\frac{7}{8}.\frac{8}{9}.\frac{9}{10}\)

\(S=\frac{1}{10}\)

học tốt 

S=\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.......\frac{9}{10}\)

S=\(\frac{1.2.3....9}{2.3.4...10}=\frac{1}{10}\)

Vậy S=\(\frac{1}{10}\)

\(S=\frac{1}{2}:\frac{3}{2}:\frac{4}{3}:\frac{5}{4}:\frac{6}{5}:\frac{7}{6}:\frac{8}{7}:\frac{9}{8}:\frac{10}{9}\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}.\frac{6}{7}.\frac{7}{8}.\frac{8}{9}.\frac{9}{10}\)

\(=\frac{1.2.3.4.5.6.7.8.9}{2.3.4.5.6.7.8.9.10}\)

\(=\frac{1}{10}\)

\(=\frac{4}{25}\left(\frac{5}{9}+\frac{-10}{3}\right)+\frac{52}{9}\)

\(=\frac{4}{25}.\frac{-25}{9}+\frac{52}{9}\)

\(=\frac{-4}{9}+\frac{52}{9}=\frac{16}{3}\)

\(\frac{4}{25}\cdot\frac{5}{9}+\frac{-4}{25}\cdot\frac{10}{3}+5\frac{7}{9}\)

\(=\frac{4}{45}-\frac{8}{15}+\frac{52}{9}\)

\(=\frac{4}{45}-\frac{24}{45}+\frac{260}{45}\)

\(=\frac{240}{45}=\frac{16}{3}\)

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