Ta có : 

1/6 < 1/5 , 1/7 < 1/5 , ... 1/19 < 1/5

=> 1/6 + 1/7 + ...+ 1/19 < 1/5 + 1/5 + ...+ 1/5

=> 1/6 + 1/7 + ...+ 1/19  < 1/5 . 14 

=> 1/6 + 1/7 + ...+ 1/19 < 14/5 = 2 , 8 

Đặt C\(=\frac{1}{6}+\frac{1}{7}+...+\frac{1}{19}\)

\(\)C có 13 phân số tất cả, ta chia ra như sau: 
C =1/5+(1/6+....1/11)+(1/12+1/12+.....1/16 +1/17) 
Vì trong nhóm I thì 1/ 6 là lớn nhất, nhóm II thì 1/12 là lớn nhất ,xuy ra: 
C< 1/5 +6.1/6+6.1/12 
C<1/5+ 1 +1/2 
C<1+7/10<1+1=2 
Vậy C<2

1/6+1/7+...1/19

=(1/6+1/7+...+1/13)+(1/14+1/15+...+1/19)< 7.1/6+6.1/14

=7/6+6/14

=67/42<84/42=2

=> 1/6+1/7+...+1/19<2

k minh nha

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: ‐﴾‐a+b+c﴿+﴾b+c‐1﴿

=a‐b‐c+b+c‐1

=﴾b‐b﴿+﴾c‐c﴿+a‐1

=0+0+a‐1

=a‐1

﴾b‐c+6﴿‐﴾7‐a+b﴿+c

=b‐c+6‐7+a‐b+c =

﴾b‐b﴿+﴾c‐c﴿+a+[﴾‐7﴿+6]

=0+0+a‐1

=a‐1

Vì a‐1=a‐1

=>‐﴾‐a+b+c﴿+﴾b+c‐1﴿=﴾b‐c+6﴿‐﴾7‐a+b﴿‐c 

B=(1/4+1/5+1/6+1/7)+...+(1/16+1/17+1/18+1/19)

1/4+1/5+1/6+1/7>4*1/7=4/7

1/8+1/9+1/10+1/11>4*1/11=4/11

...

1/16+1/17+1/19+1/19>4/19

=>B>4(1/7+1/11+1/15+1/19)>1

B=1/4 + 1/5 +....+ 1/19

B= (1/4 + 1/5 +...+ 1/9) + (1/10 + 1/11 +...+1/19)

Ta có: 1/4 + 1/5 +...+ 1/9 > 1/9 + 1/9 +...+ 1/9

        1/10 + 1/11 +...+ 1/19 > 1/19 + 1/19 +...+ 1/19

ban lam dung roi