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17 tháng 4 2018

S = 3/1x4 + 3/4x7 +...+ 3/10x13 + 3/13x16

S = 1/1 - 1/4 + 1/4 - 1/7 +...+ 1/10 - 1/13 + 1/13 - 1/16

S = 1 + (-1/4 + 1/4) + (-1/7 + 1/7) +...+ (-1/10 + 1/10) + (-1/13 + 1/13) - 1/16

S = 1 +         0         +         0        +...+            0          +           0           - 1/16

S = 1 - 1/16

S = 16/16 - 1/16

S = 15/16

So sánh: 15/16 với 1

vì 15<16

nên 15/16<1

vậy tổng S < 1

17 tháng 4 2018

3S=1/3(1/1 - 1/4 + 1/4 - 1/7+...+1/13 - 1/16)

3S=1/3(1/1 - 1/16)

3S=1/3 x 15/16

  S=15/16

27 tháng 1 2016

1/1.4+1/4.7+1/7.10+1/10.13+1/13.16

=1/3.(3/1.4+3/4.7+3/7.10+3/10.13+3/13.16)

=1/3.(1/1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)

=1/3.(1/1-1/16)

=1/3.(16/16-1/16)=1/3.15/16=5/16

21 tháng 4 2016

S=3/1.4+3/4.7+3/7.10+.....+3/40.43+3/43.46

S= 1/1-1/4+1/4-1/7+1/7-1/10+...+1/40-1/43+1/43-1/46

S= 1-1/46

=> S<1

24 tháng 4 2016

S=3.(1/1-1/4+1/4-1/7+.........+1/40-1/43+1/43-1/46)          

S=3.(1/1-1/46)

S=3.45/46

S=2/43/46

=> 2/43/46>1

=>S>1

1 tháng 5 2015

= 1/1-1/4+1/4-1/7+1/7-1/10+...+1/40-1/43+1/43-1/46

= 1 - 1/46 = 45/46 < 1

23 tháng 4 2016

Cho S=3/1x4+3/4x7+3/7x10+...+3/40x43+3/43x46. Hãy chứng tỏ S<1

ĐPM : S < 1

23 tháng 4 2016

S=3/1x4+3/4x7+3/7x10+...+3/40x43+3/43x46

\(S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{43}-\frac{1}{46}\)

\(S=1-\frac{1}{46}\)

=>S<1

30 tháng 4 2016

\(S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{43}-\frac{1}{46}\)

\(S=1-\frac{1}{46}<1\)

=>chứng minh bị sai hoặc đề sai

30 tháng 4 2016

S=\(\frac{3}{1.4}+\frac{3}{4.7}+...........+\frac{3}{43.46}\)

=\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...........+\frac{1}{43}-\frac{1}{46}\)

=\(1-\frac{1}{46}<1\)

\(\Rightarrow S<1\)

=1-1/4+1/4-1/7+1/7-...+1/37-1/40

=1-1/40=39/40

21 tháng 5 2022

Mình cần gấp ạ. Mốt mik thi rồi

Tính nhanh.\(\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{57.40}\)

\(=5.\frac{1}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{4}{37.40}\right)\)

\(=\frac{5}{3}\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{37}-\frac{1}{40}\right)\)

\(=\frac{5}{3}\left(\frac{1}{1}-\frac{1}{40}\right)\)

\(=\frac{5}{3}.\frac{39}{40}\)

\(=\frac{13}{8}\)

Rút gobj p/s

\(\frac{2019.2020+4038}{2022.2011-4044}\)

\(=\frac{2019.\left(2020+2\right)}{2020.\left(2011-2\right)}\)

\(=\frac{2019.2022}{2022.2019}\)

\(=\frac{1}{1}=1\)

Study well 

Cho mk sorry nha dong thứ 2 từ trên cuống dưới phải là 

\(5.\frac{1}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{37.40}\right)\) nha 

Sorry nhiều 

Study well 

21 tháng 1 2020

Ta có:

S=\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)

S=\(1-\frac{1}{n+3}\)

=>S<1

Vậy S<1

\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)

21 tháng 1 2020

Sory mình bấm bị lỗi