Tính nhanh
A=111/110+91/90+73/72+…………+21/20+13/12+7/6+3/2
K
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NT
0
LH
2
SN
1
NL
Nguyễn Lê Phước Thịnh
CTVHS
23 tháng 5 2022
\(=1+1+1+1+1+1+1+1+1+\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)\)
\(=9+\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)
=9+9/10=99/10
TG
23 tháng 10 2016
Gọi tổng dãy số hạng trên là A
A = 1 + \(\frac{1}{2}\)+ 1 + \(\frac{1}{6}\)+ 1 + \(\frac{1}{12}\)+ ... + 1 + \(\frac{1}{90}\)+ 1 + \(\frac{1}{110}\)
Mà từ \(\frac{1}{2}\)đén \(\frac{1}{110}\) có 10 số
A = 1 x 10 + \(\frac{1}{2}\)+( \(\frac{1}{2}\)- \(\frac{1}{3}\)) + ( \(\frac{1}{3}\)-\(\frac{1}{4}\)) + (\(\frac{1}{4}\)-\(\frac{1}{5}\)) + ... + \(\frac{1}{11}\)
A = 10 + \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{11}\)= \(\frac{112}{11}\)
D
1 tháng 5 2015
= \(\left(1+\frac{1}{2}\right)+\left(1+\frac{1}{6}\right)+\left(1+\frac{1}{12}\right)+....+\left(1+\frac{1}{90}\right)\)
= \(\left(1+1+1+....+1\right)+\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+....+\frac{1}{90}\right)\)(9 số 1)
= 9 + \(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{9.10}\right)\)
= \(9+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\right)\)
= \(9+\left(1-\frac{1}{10}\right)=9+\frac{9}{10}=\frac{90}{10}+\frac{9}{10}=\frac{99}{10}\)
PT
3
13 tháng 8 2015
\(2x+1+\frac{1}{6}+1+\frac{1}{12}+..+1+\frac{1}{90}=10\)
=> 2x + 8 + \(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}=10\)
=> 2x + \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}=10-8\)
\(2x+1-\frac{1}{10}=2\)
=> 2x + \(\frac{9}{10}=2\)
=> 2x = 2 - 9/10
=>2x = 11/10
=> x = 11/10 : 2
x = 11/20
M
1
NL
Nguyễn Lê Phước Thịnh
CTVHS
20 tháng 9 2025
Ta có: \(2x+\frac76+\frac{13}{12}+\frac{21}{20}+\frac{31}{30}+\frac{43}{42}+\frac{57}{56}+\frac{73}{72}+\frac{91}{90}=10\)
=>\(2x+1+\frac16+1+\frac{1}{12}+\ldots+1+\frac{1}{90}=10\)
=>\(2x+8+\left(\frac16+\frac{1}{12}+\cdots+\frac{1}{90}\right)=10\)
=>\(2x+8+\left(\frac12-\frac13+\frac13-\frac14+\cdots+\frac19-\frac{1}{10}\right)=10\)
=>\(2x+8+\left(\frac12-\frac{1}{10}\right)=10\)
=>\(2x+8+\frac{4}{10}=10\)
=>\(2x=10-8-\frac{4}{10}=2-\frac{4}{10}=2-\frac25=\frac85\)
=>\(x=\frac85:2=\frac45\)
VA
0
EC
2
A = 1 + 1/110 + 1 + 1/90 + ... + 1 + 1 /2
A = 10 + 1/1.2+ 1 /2.3 + ... + 1/9.10 + 1/10.11
A = 10 + 1/1 - 1/2 + 1 /2 - 1/3 + ... + 1/9 - 1/10 + 1/10 - 1/11
A = 10 + 1/1 - 1/11
A = 10 + 10/11
A = 120/11
A = \(\frac{111}{110}+\frac{91}{90}+\frac{73}{72}+...+\frac{13}{12}+\frac{7}{6}+\frac{3}{2}\)
A = \(\left(\frac{1}{2}+1\right)+\left(\frac{1}{6}+1\right)+\left(\frac{1}{12}+1\right)+....+\left(\frac{1}{110}+1\right)\)
A = (1 + 1 + 1 +...+ 1) + \(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)\)
A = 10 + \(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)
A = \(10+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)\)
A = \(10+\left(1-\frac{1}{11}\right)\)
A = \(10+\frac{10}{11}\)
A = \(\frac{120}{11}\)