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

\(=1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{90}\)

\(=1+\left(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+.....+\frac{2}{9.10}\right)\)

\(=1+2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{9.10}\right)\)

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

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

\(=1+1-\frac{1}{5}\)(nhân phá ngoặc)

\(=2-\frac{1}{5}\)< 2 

Vậy K = \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.....+\frac{1}{45}\)< 2

                            K CHO MK NHA

                                       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

.

\(S=1+\frac{1}{3}+...+\frac{1}{45}\) 

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

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

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

\(\Rightarrow S<2\)

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 

=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

Ta co:\(A=\frac{1}{2.2}+\frac{1}{4.4}+\frac{1}{6.6}+...+\frac{1}{14.14}< \frac{2}{2.4}+\frac{2}{4.6}+\frac{1}{6.8}+...+\frac{2}{14.16}\left(1\right)\)

\(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{14.16}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{16}\)

\(=\frac{1}{2}-\frac{1}{16}=\frac{7}{16}< \frac{8}{16}=\frac{1}{2}\left(2\right)\)

\(\left(1\right),\left(2\right)\Rightarrow A< \frac{1}{2}\)

V...

cho dong dau tien la dau =,chu ko phai dau < nhe

Cảm ơn  bạn nhiều 

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