2/12.6/22.12/32.20/42....110/102.x=-20
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26 tháng 5 2020
\(S=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{110}\)
\(S=\frac{2}{4\cdot5}+\frac{2}{5\cdot6}+...+\frac{2}{10\cdot11}\)
\(S=2\left(\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{10\cdot11}\right)\)
\(S=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{10}-\frac{1}{11}\right)\)
\(S=2\left(\frac{1}{4}-\frac{1}{11}\right)=2\cdot\frac{7}{44}=\frac{7}{22}\)
XO
14 tháng 10 2019
Ta có : \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}\)
\(=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{10\times11}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)
\(=1-\frac{1}{11}\)
\(=\frac{10}{11}\)
VH
14 tháng 10 2019
Đặt A=\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{110}\)
=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{10.11}\)
=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{10}-\frac{1}{11}\)
=\(1-\frac{1}{11}\)
=\(\frac{10}{11}\)
Vậy...
15 tháng 9 2019
\(\frac{x+110}{100}+\frac{x+8}{102}+\frac{x+6}{104}=\frac{x+4}{106}+\frac{x+2}{108}\)
\(\Leftrightarrow\frac{x+110}{100}+\left(\frac{x+8}{102}+1\right)+\left(\frac{x+6}{104}+1\right)=\left(\frac{x+4}{106}+1\right)+\left(\frac{x+2}{108}+1\right)\)
\(\Leftrightarrow\frac{x+110}{100}+\frac{x+110}{102}+\frac{x+110}{104}=\frac{x+110}{106}+\frac{x+110}{108}\)
\(\Leftrightarrow\frac{x+110}{100}+\frac{x+110}{102}+\frac{x+110}{104}-\frac{x+110}{106}-\frac{x+110}{108}=0\)
\(\Leftrightarrow\left(x+110\right)\left(\frac{1}{100}+\frac{1}{102}+\frac{1}{104}+\frac{1}{106}+\frac{1}{108}\right)=0\)
\(\Leftrightarrow x+110=0\) (vì \(\frac{1}{100}+\frac{1}{102}+\frac{1}{104}-\frac{1}{106}-\frac{1}{108}>0\))
\(\Leftrightarrow x=-110\)
Vậy \(x=-110\)
HT
4
17 tháng 7 2015
B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + ... + 1/110
B = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + .... + 1/10.110
B = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/10 - 1/11
B = 1 - 1/11
B = 10/11
DH
17 tháng 7 2015
B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + .... + 1/110
=1/1x2 + 1/2x3 + 1/ 3x4 + 1/4x5 + 1/5 x6 + 1/ 6x 7 +.....+ 1/10 x11
=1-1/2 + 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7 +......+ 1/10 - 1/11
= 1 + (1/2-1/2)+(1/3-1/3)+(1/4-1/4)+(1/5-1/5)+(1/6-1/6)+.....+(1/10-1/10)-1/11
= 1- 1/11=10/11
Vậy B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + .... + 1/110 = 10/11
MP
1
18 tháng 7 2015
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{90}+\frac{1}{110}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{9.10}+\frac{1}{10.11}\)
=\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...\frac{1}{7}-\frac{1}{8}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(=1-\frac{1}{8}+\frac{1}{9}-\frac{1}{11}\)
\(=\frac{709}{792}\)
PT
4
HH
19 tháng 6 2018
Giải:
\(\dfrac{1}{3}-\dfrac{1}{12}-\dfrac{1}{20}-...-\dfrac{1}{90}-\dfrac{1}{110}=x-\dfrac{5}{13}\)
\(\Leftrightarrow\dfrac{1}{1.3}-\dfrac{1}{3.4}-\dfrac{1}{4.5}-...-\dfrac{1}{9.10}-\dfrac{1}{10.11}=x-\dfrac{5}{13}\)
\(\Leftrightarrow\dfrac{-1}{2}\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}\right)=x-\dfrac{5}{13}\)
\(\Leftrightarrow\dfrac{-1}{2}\left(\dfrac{1}{1}-\dfrac{1}{11}\right)=x-\dfrac{5}{13}\)
\(\Leftrightarrow\dfrac{-1}{2}.\dfrac{10}{11}=x-\dfrac{5}{13}\)
\(\Leftrightarrow\dfrac{-5}{11}=x-\dfrac{5}{13}\)
\(\Leftrightarrow\dfrac{-5}{11}+\dfrac{5}{13}=x\)
\(\Leftrightarrow x=\dfrac{-10}{143}\)
Vậy ...
NT
4
BD
6 tháng 4 2017
TA THẤY
2=1x2
6=2x3
12=3x4
20=4x5
30=5x6
42=6x7
qui luật là các số hạng trong dãy đều bằng số số hạng của nó nhân với số hang của số đứng liền sau nó
vậy số thứ 102 là :
102x103=10506
ko có chi nha bạn đừng ngại
LX
3
20 tháng 8 2017
\(\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{12}+\dfrac{5}{20}+\dfrac{5}{30}+\dfrac{5}{42}+...+\dfrac{5}{110}\)
\(=\dfrac{5}{1.2}+\dfrac{5}{2.3}+\dfrac{5}{3.4}+\dfrac{5}{4.5}+\dfrac{5}{5.6}+\dfrac{5}{6.7}+...+\dfrac{5}{10.11}\)
\(=\dfrac{5}{1}-\dfrac{5}{2}+\dfrac{5}{2}-\dfrac{5}{3}+\dfrac{5}{3}-\dfrac{5}{4}+\dfrac{5}{4}-\dfrac{5}{5}+...+\dfrac{5}{10}-\dfrac{5}{11}\)
\(=\dfrac{5}{1}-\dfrac{5}{11}=\dfrac{50}{11}\)
DH
20 tháng 8 2017
=5(1/2+1/6+1/12+1/20+1/30+1/42+...+1/110)
=5(1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/10.11)
=5(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/10-1/11)
=5(1-1/11)=5.10/11=50/11
\(\dfrac{2}{1^2}.\dfrac{6}{2^2}.\dfrac{12}{3^2}.\dfrac{20}{4^2}.....\dfrac{110}{10^2}.x=-20\)
\(\dfrac{1.2}{1^2}.\dfrac{2.3}{2^2}.\dfrac{3.4}{3^2}.\dfrac{4.5}{4^2}.....\dfrac{10.11}{10^2}.x=-20\)
\(\dfrac{1.2.2.3.3.4.4.5.5.....10.10.11}{1.1.2.2.3.3.4.4.5.5.....10.10}.x=-20\)
\(11.x=-20\)
\(x=-20:11=-\dfrac{20}{11}\)
\(\dfrac{2}{1^2}\cdot\dfrac{6}{2^2}\cdot\dfrac{12}{3^2}\cdot\dfrac{20}{4^2}\cdot...\cdot\dfrac{110}{10^2}\cdot x=-20\)
\(\Leftrightarrow\dfrac{1\cdot2}{1\cdot1}\cdot\dfrac{2\cdot3}{2\cdot2}\cdot\dfrac{3\cdot4}{3\cdot3}\cdot\dfrac{4\cdot5}{4\cdot4}\cdot...\cdot\dfrac{10\cdot11}{10\cdot10}\cdot x=-20\)
\(\Leftrightarrow\dfrac{1\cdot2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot5\cdot...\cdot10\cdot11}{1\cdot1\cdot2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot...\cdot10\cdot10}\cdot x=-20\)
\(\Rightarrow11\cdot x=-20\)
\(\Rightarrow x=\dfrac{-20}{11}\)
Vậy \(x=\dfrac{-20}{11}\).