\(\frac{1}{20x23}\)+\(\frac{1}{23x26}\)+...+\(\frac{1}{77x80}\)< \(\frac{1}{9}\)
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
15 tháng 6 2023
A=1/20*23+1/23*26+...+1/77*80
=1/3(1/20-1/23+1/23-1/26+...+1/77-1/80)
=1/3*3/80=1/80<1/79
H
1
16 tháng 4 2018
Đặt \(A=\frac{3^2}{20.23}+\frac{3^2}{23.26}+...+\frac{3^2}{77.80}\) ta có :
\(A=3\left(\frac{3}{20.23}+\frac{3}{23.26}+...+\frac{3}{77.80}\right)\)
\(A=3\left(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+...+\frac{1}{77}-\frac{1}{80}\right)\)
\(A=3\left(\frac{1}{20}-\frac{1}{80}\right)\)
\(A=3.\frac{3}{80}\)
\(A=\frac{9}{80}< 1\) ( tử bé hơn mẫu )
Vậy \(A< 1\)
Chúc bạn học tốt ~
TU
1
TN
12 tháng 4 2016
đặt A=9/20x23+9/23x26+...+9/77x80
<=>\(A=3\left(\frac{3}{20\cdot23}+\frac{3}{23\cdot26}+...+\frac{3}{77\cdot80}\right)\)
\(\Rightarrow A=3\left(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+...+\frac{1}{77}-\frac{1}{80}\right)\)
\(\Rightarrow A=3\left(\frac{1}{20}-\frac{1}{80}\right)\)
\(\Rightarrow A=3\cdot\frac{3}{80}\)
\(\Rightarrow A=\frac{9}{80}\)
DT
3
TN
18 tháng 4 2016
đặt A=32/20x23+32/23x26+...+32/77x80
\(A=3\left(\frac{3}{20\cdot23}+\frac{3}{23\cdot26}+...+\frac{3}{77\cdot80}\right)\)
\(=3\left(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+...+\frac{1}{77}-\frac{1}{80}\right)\)
\(=3\left(\frac{1}{20}-\frac{1}{80}\right)\)
\(=3\cdot\frac{3}{80}\)
\(=\frac{9}{80}\)
2 tháng 2 2019
a) \(\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+...+\frac{1}{2007x2009}\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2007}-\frac{1}{2009}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{2009}\right)=\frac{1}{2}\cdot\frac{2008}{2009}=\frac{1004}{2009}\)
....
các bài cn lại bn lm tương tự nha
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
19 tháng 8 2023
b, \(\dfrac{1}{18}+\dfrac{1}{54}+\dfrac{1}{108}+...+\dfrac{1}{990}\)
3A = \(\dfrac{1}{6}+\dfrac{1}{18}+...+\dfrac{1}{330}\)
3A-A = \(\dfrac{1}{6}-\dfrac{1}{990}\)
2A = 82/495
A =82/495 : 2
A=41/495
TH
5
SF
18 tháng 8 2018
\(\frac{1}{11×14}+\frac{1}{14×17}+\frac{1}{17×20}+\frac{1}{20×23}+\frac{1}{23×26}\)
\(=\frac{1}{3}×\left(\frac{3}{11×14}+\frac{3}{14×17}+\frac{3}{17×20}+\frac{3}{20×23}+\frac{3}{23×26}\right)\)
\(=\frac{1}{3}×\left(\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{23}-\frac{1}{26}\right)\)
\(=\frac{1}{3}×\left(\frac{1}{11}-\frac{1}{26}\right)\)
\(=\frac{1}{3}×\frac{15}{286}\)
\(=\frac{5}{286}\)
18 tháng 8 2018
\(\frac{1}{11\times14}+\frac{1}{14\times17}+\frac{1}{17\times20}+\frac{1}{20\times23}+\frac{1}{23\times26}\)
\(=\frac{1}{3}\times\left(\frac{1}{11\times14}+\frac{1}{14\times17}+\frac{1}{17\times20}+\frac{1}{20\times23}+\frac{1}{23\times26}\right)\)
\(=\frac{1}{3}\times\left(\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}+\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}\right)\)
\(=\frac{1}{3}\times\left(\frac{1}{11}-\frac{1}{26}\right)\)
= 5/286
7 tháng 6 2018
\(=\frac{1}{3}x\left(\frac{3}{1x4}+\frac{3}{4x7}+...+\frac{3}{77x80}\right)\)
\(=\frac{1}{3}x\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{77}-\frac{1}{80}\right)\)
\(=\frac{1}{3}x\left(\frac{1}{1}-\frac{1}{80}\right)\)
\(=\frac{1}{3}\times\frac{79.}{80}\)
\(=\frac{79}{240}\)
Tk giúp mk nha cảm ơn !!
KM
1
\(\frac{1}{20\cdot23}+\frac{1}{23\cdot26}+...+\frac{1}{77\cdot80}\)
\(=\frac{1}{3}\left[\frac{3}{20\cdot23}+\frac{3}{23\cdot26}+...+\frac{3}{77\cdot80}\right]\)
\(=\frac{1}{3}\left[\frac{1}{20}-\frac{1}{23}+...+\frac{1}{77}-\frac{1}{80}\right]\)
\(=\frac{1}{3}\left[\frac{1}{20}-\frac{1}{80}\right]\)
\(=\frac{1}{3}\left[\frac{4}{80}-\frac{1}{80}\right]\)
\(=\frac{1}{3}\cdot\frac{3}{80}=\frac{1}{1}\cdot\frac{1}{80}=\frac{1}{80}\)
Mà \(\frac{1}{80}< \frac{1}{9}\)nên \(\frac{1}{20\cdot23}+\frac{1}{23\cdot26}+...+\frac{1}{77\cdot80}< \frac{1}{9}\)
Vậy : ...
\(\frac{1}{20.23}+\frac{1}{23.26}+...+\frac{1}{77.80}\)
\(=\frac{1}{3}.\left(\frac{3}{20.23}+\frac{3}{23.26}+...+\frac{3}{77.80}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+...+\frac{1}{77}-\frac{1}{80}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{20}-\frac{1}{80}\right)\)
\(=\frac{1}{3}.\frac{3}{80}\)
\(=\frac{1}{80}< \frac{1}{9}\)