Vi 10/17<1

8/15<1

11/16<1

Suy ra 10/17+11/16+8/15 <2

10/17+8/15+11/16=1,809068627 ko tin ra hết quả này thì cứ bấm máy tính đi 

=>1,809068627  \(<\)2

ủng hộ nhiều vào nha 

hoac vi 10/17< 2

8/15<2

11/16<2

=>10/17+8/15+11/16\(<\)2

10/17+ 8/15 + 11/16=2400 / 4081+2176 / 4080 +2805 / 4080 = 7381/4080
mà 8160 / 4080 mới bằng 2 
suy ra 7381 / 4080 < 2 vì 7381< 8160
hay 10/17+8/15+11/16 < 2

Lời giải:

a, Ta có: \(A=\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+...+\frac{1}{22}>\frac{1}{22}+\frac{1}{22}+\frac{1}{22}+\frac{1}{22}+...+\frac{1}{22}=\frac{1}{22}.11=\frac{11}{22}=\frac{1}{2}\)

Vậy: \(A>\frac{1}{2}\)

b, Ta có: \(B=\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{99}+\frac{1}{100}\)

\(=\left(\frac{1}{10}+\frac{1}{11}+...+\frac{1}{49}+\frac{1}{50}\right)+\left(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{99}+\frac{1}{100}\right)\)

Mà: \(\left(\frac{1}{10}+\frac{1}{11}+...+\frac{1}{49}+\frac{1}{50}\right)+\left(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{99}+\frac{1}{100}\right)\text{​​}\text{​​}\text{​​}>\left(\frac{1}{50}+...+\frac{1}{50}+\frac{1}{50}\right)+\left(\frac{1}{100}+...+\frac{1}{100}+\frac{1}{100}\right)\)

=> \(B\text{​​}\text{​​}\text{​​}>\frac{1}{50}.41+\frac{1}{100}.50=\frac{41+25}{50}=\frac{33}{25}>1\)

Vậy: \(B>1\)

c, Ta có: \(C=\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+...+\frac{1}{16}+\frac{1}{17}< \frac{1}{5}+\frac{1}{6}+\left(\frac{1}{7}+...+\frac{1}{7}+\frac{1}{7}\right)=\frac{11}{30}+11.\frac{1}{7}=\frac{407}{210}< \frac{420}{210}=2\)

Vậy: \(C< 2\)

Chúc bạn học tốt!Tick cho mình nhé!

ta có: \(\frac{10}{27}< \frac{10}{30}=\frac{1}{3}\)

\(\frac{9}{16}< \frac{9}{9}=1\)

\(\frac{11}{34}< \frac{11}{22}=\frac{1}{2}\)

=>A<\(\frac{1}{3}+1+\frac{1}{2}\)<2

vậy A<2

Sửa đề : CMR \(10^{15}+10^{16}+10^{17}\vdots 111\)

Lời giải:

Ta có:

\(10^{15}+10^{16}+10^{17}=10^{15}+10^{15+1}+10^{15+2}\)

\(=10^{15}+10^{15}.10+10^{15}.10^2\)

\(=10^{15}(1+10+10^2)=10^{15}.111\vdots 111\) (đpcm)