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

\(S=1+\frac{1}{3}+...+\frac{1}{45}\) 

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

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

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

\(\Rightarrow S<2\)

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                                       Giải

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

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

=>S=2/1x2 + 2/2x3 +2/3x4+......+2/9x10

=>S=2x(1/1x2  + 1/2x3  +....+1/9x10)

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

=>S=2x(1/1 - 1/10)

Vì 1/1-1/10<1=>2x(1/1 - 1/10)>2x1=2

Hay 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 

S=1/2+1/3+1/4+1/5+1/6+1/7+1/8=

                                                     =481/280=1,717(857142)

                                                   => S<2

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

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

\(\frac{S}{2}=\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)

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

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

\(S=\frac{9}{5}