\(S=1+\frac{1}{3}+...+\frac{1}{45}\) 

\(\frac{S}{2}=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{9.10}=1-\frac{1}{2}+\frac{1}{2}-...+\frac{1}{9}-\frac{1}{10}\) 

\(\frac{S}{2}=1-\frac{1}{10}=\frac{9}{10}\) 

\(\Rightarrow S=\frac{9.2}{10}=1.8<2\) 

\(\Rightarrow S<2\)

Chúc bạn học tốt nha !!!

S = 2/2  + 2/6  + 2/12 + 2/20 + ... + 2/90

S = 2/1.2 + 2/2.3 + 2/3.4 + .. + 2/9.10 

=> S = 2( 1/1.2 + 1/2.3 + ... + 1/9.10)

=> S = 2 ( 1/1 - 1/2 + 1/2  - 1/3 + .. + 1/9 - 1/10 )

=> S = 2 ( 1/1 - 1/10 ) 

Vì 1/1 - 1/10 < 1 => 2 ( 1/1 - 1/0 ) < 2.1 = 2 

VẬy S < 2 

tick đúng nha 

So sánh s với 2 biếts=1+13 +16 +110 +............+145 

Như vậy ta sẽ so sánh 1 và 1/3 + 1/6 + 1/10 +......+ 1/45

Ta có :  1/3 + 1/6 + 1/10 + .....+  1/45 <  1/10 + 1/10 + 1/10 +......+  1/10 

Mà 1/10 + 1/10 + 1/10 + ....+  1/10 = 8/10 < 1

     Vậy S <2

S = 1 + 1/3 + 1/6 + 1/10 + ... + 1/45

S = 2/2 + 2/6 + 2/12 + 2/20 + ... + 2/90

S = 2 × (1/1×2 + 1/2×3 + 1/3×4 + ... + 1/9×10)

S = 2 × (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10)

S = 2 × (1 - 1/10) < 2 × 1 = 2

=> S < 2

Ta có

\(\frac{S}{2}=2+\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{90}\)

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

\(\Rightarrow\frac{S}{2}=2+\frac{1}{2}-\frac{1}{10}\)

\(\Rightarrow\frac{S}{2}=2+\frac{2}{5}=\frac{12}{5}\)

\(\Rightarrow\frac{S}{2}=\frac{6}{5}< 2\)

=> S<2

\(S=1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\)

\(S=\frac{2}{2}+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{90}\)

\(S=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{9.10}\)

\(S=2\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{9.10}\right)\)

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

\(S=2\left(1-\frac{1}{10}\right)\)

có : \(1-\frac{1}{10}< 1\Rightarrow2\left(1-\frac{1}{10}\right)< 2.1\)

Vậy: \(S< 2\)

hư!hu! mấy ông chs bẩn! Nhân lúc t giải bài khác đi giải bài này trước t 

\(K=1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{1}{45}\)

\(K=1+\frac{1}{\frac{2\cdot3}{2}}+\frac{1}{\frac{3\cdot4}{2}}+\frac{1}{\frac{4\cdot5}{2}}+....+\frac{1}{\frac{9\cdot10}{2}}\)

\(K=1+\left[2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{9}-\frac{1}{10}\right)\right]\)

\(K=1+\left[2\left(\frac{1}{2}-\frac{1}{10}\right)\right]\)

\(K=1+\left(2\cdot\frac{2}{5}\right)=1+\frac{4}{5}=\frac{9}{5}\)

Vì \(\frac{9}{5}< 2\)\(\Rightarrow K< 2\)

\(K=1+\frac{2}{6}+\frac{2}{12}+...+\frac{2}{90}\)

\(K=1+\left(\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(K=1+\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(K=1+\frac{2}{5}\)

\(K=\frac{7}{5}\)

Vì 1+2/5<2

=>K<2

=1/2.(1+1/3+1/6+...+1/45)

=1/2+1/6+1/12+1/20+...+1/90

=1/1.2+1/2.3+1/3.4+...+1/9.10

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

=1-1/10

=9/10

dung do..k hegg