\(S=\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{184}+\frac{1}{238}+\frac{1}{340}=\frac{1}{3}\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}\right)\)

\(=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\right)\)

\(=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{20}\right)=\frac{1}{3}.\frac{9}{20}=\frac{3}{20}>\frac{2}{20}=\frac{1}{10}=0,1\)

vậy S>0,1

S = \(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\)

S = \(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+\frac{1}{17.20}\)

S = \(\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+....+\frac{1}{17}-\frac{1}{20}\right)\)

S = \(\frac{1}{3}\left(\frac{1}{2}-\frac{1}{20}\right)=\frac{1}{3}.\frac{9}{20}\)

S = \(\frac{3}{20}\)

S = 0,15 > 0,1

S=\(\frac{3}{20}\)>0,1

li ke cho mình nha

\(A=\frac{9}{10}+\frac{39}{40}+\frac{87}{88}+\frac{153}{154}+\frac{237}{238}+\frac{339}{340}=\frac{117}{20}\)

\(suyra:A<1\)

S=1/2.5 + 1/5.8 + 1/8.11 + 1/11.14 + 1/14.17 + 11/17.20

S=1/3.(1/2-1/5+1/5-1/8+.......+1/17 - 1/20)

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

S=1/3.9/20

S=3/20 

Ai tích mk mk sẽ tích lại    

Chú ý tích gấp ddooi khi tích đủ 3 cái 

S=1/2.5 + 1/5.8 + 1/8.11 + 1/11.14 + 1/14.17 + 11/17.20

S=1/3.(1/2-1/5+1/5-1/8+.......+1/17 - 1/20)

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

S=1/3.9/20

S=3/20 

Ta có: S = 1/10 + 1/40 + 1/88 + 1/154 + 1/238 + 1/340
=> S = 1/2.5 + 1/5.8 + 1/8.11 + 1/11.14 +1/14.17 +1/17.20
Nhân 2 vế với 3 và áp dụng công thức tách 1 phân số thành hiệu 2 phân số:
x/n.(n + x) = 1/n – 1/(n + x)
=> 3.S = 3.(1/2.5 + 1/5.8 + 1/8.11 +1/11.14 +1/14.17 +1/17.20)
=> 3.S = 3/2.5 + 3/5.8 + 3/8.11 + 3/11.14 +3/14.17 +3/17.20
=> 3.S = 1/2 – 1/ 5 + 1/5 – 1/8 + 1/8 – 1/11 + 1/11 – 1/14 + 1/14 – 1/17 + 1/17 -1/20
=> 3.S = 1/2 – 1/20
=> 3.S = 9/20
=> S = 3/20

Ta có: S = 1/10 + 1/40 + 1/88 + 1/154 + 1/238 + 1/340 + 1/460 + 1/598 + 1/754 + 1/928 
=> S = 1/2.5 + 1/5.8 + 1/8.11 + ... + 1/26.29 + 1/29.32 
Nhân 2 vế với 3 và áp dụng công thức tách 1 phân số thành hiệu 2 phân số: x/n.(n + x) = 1/n - 1/(n + x) 
=> 3.S = 3.(1/2.5 + 1/5.8 + 1/8.11 + ... + 1/26.29 +1/29.32) 
=> 3.S = 3/2.5 + 3/5.8 + 3/8.11 + ... + 3/26.29 + 3/29.32 
=> 3.S = 1/2 - 1/ 5 + 1/5 - 1/8 + 1/8 - 1/11 + ... + 1/26 - 1/29 + 1/29 - 1/32 
=> 3.S = 1/2 - 1/32 
=> 3.S = 15/32 
=> S = 5/32

@Cre: G+ 

S=1/2.5 + 1/5.8 + 1/8.11 + 1/11.14 + 1/14.17 + 11/17.20

S=1/3.(1/2-1/5+1/5-1/8+.......+1/17 - 1/20)

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

S=1/3.9/20

S=3/20 

S=5/32 nhé

ai k mình sẽ k lại

a) A = 1/2.5 + 1/5.8 + 1/8.11 + 1/11.14 + 1/14.17 + 1/17.20

=> 3A = 1/2 - 1/5 + 1/5 - .... + 1/14 - 1/17 + 1/17 - 1/20

=> 3A = 1/2 - 1/20 = 9/20

=> A = 3/20

b) 2004¹⁰ + 2004⁹ = 2004⁹(1+2004) = 2004⁹ . 2005

2005¹⁰  = 2005⁹  . 2005

Do 2005⁹ > 2004⁹ nên 2004¹⁰ + 2004⁹ < 2005¹⁰

Ta có : \(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\)

\(=\frac{1}{2\times5}+\frac{1}{5\times8}+\frac{1}{8\times11}+\frac{1}{11\times14}+\frac{1}{14\times17}+\frac{1}{17\times20}\)

\(=\frac{1}{3}\times\left(\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+\frac{3}{14\times17}+\frac{3}{17\times20}\right)\)

\(=\frac{1}{3}\times\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\right)\)

\(=\frac{1}{3}\times\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(=\frac{1}{3}\times\frac{9}{20}\)

\(=\frac{3}{20}\)

Đặt \(A=\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\) 

=> \(A=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+\frac{1}{17.20}\)    (dấu . có nghĩa là nhân)

=> \(3A=3\left(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+\frac{1}{17.20}\right)\)

\(=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}\)

\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}\) 

\(=\frac{9}{20}\)            

Đây là kiến thức lớp 6 nhá =)) bạn mà có chỗ nào ko hiểu thì hỏi ng thầy cô giạy bạn ý