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\(C=\dfrac{-5}{7}+\dfrac{-2}{7}+\dfrac{3}{4}+\dfrac{1}{4}+\dfrac{-1}{5}=-1+1-\dfrac{1}{5}=\dfrac{-1}{5}\)
\(\dfrac{1}{3}-\dfrac{1}{12}-\dfrac{1}{20}-\dfrac{1}{30}-\dfrac{1}{42}-\dfrac{1}{56}-\dfrac{1}{72}-\dfrac{1}{90}-\dfrac{1}{110}=x-\dfrac{5}{13}\)
\(\dfrac{1}{3}\) - \(\dfrac{1}{3.4}\) - \(\dfrac{1}{4.5}\) - \(\dfrac{1}{5.6}\) - \(\dfrac{1}{6.7}\) - \(\dfrac{1}{7.8}\)- \(\dfrac{1}{8.9}\) - \(\dfrac{1}{9.10}\) - \(\dfrac{1}{10.11}\) = \(x\) - \(\dfrac{5}{13}\)
\(\dfrac{1}{3}\) - (\(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\) + \(\dfrac{1}{6.7}\)+ \(\dfrac{1}{7.8}\) + \(\dfrac{1}{8.9}\) + \(\dfrac{1}{9.10}\) + \(\dfrac{1}{10.11}\) =\(x\)-\(\dfrac{5}{13}\)
\(\dfrac{1}{3}\) - (\(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) +...+ \(\dfrac{1}{9}\) - \(\dfrac{1}{10}\) + \(\dfrac{1}{10}\) - \(\dfrac{1}{11}\)) = \(x\) - \(\dfrac{5}{13}\)
\(\dfrac{1}{3}\) - (\(\dfrac{1}{3}\) - \(\dfrac{1}{11}\)) = \(x\) - \(\dfrac{5}{13}\)
\(\dfrac{1}{3}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{11}\) = \(x\) - \(\dfrac{5}{13}\)
\(x-\dfrac{5}{13}=\dfrac{1}{11}\)
\(x\) = \(\dfrac{1}{11}\) + \(\dfrac{5}{13}\)
\(x\) = \(\dfrac{68}{143}\)
Sửa đề: 2020/1+2019/2+...+1/2020
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2021}}{\left(1+\dfrac{2019}{2}\right)+\left(1+\dfrac{2018}{3}\right)+...+\dfrac{1}{2020}+1+1}\)
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2021}}{\dfrac{2021}{2}+\dfrac{2021}{3}+...+\dfrac{2021}{2020}+\dfrac{2021}{2021}}\)
=1/2021
1/2^2 + 1/3^2 +... + 1/100^2 < 1/4 + 1/2.3 + 1/3.4 +... + 1/99.100
1/2^2 + 1/3^2 +... + 1/100^2 < 1/4 + 1/2 - 1/3 + 1/3 -1/4 +... + 1/99 + 1/100
1/2^2 + 1/3^2 +... + 1/100^2 < 1/4 + 1/2 - 1/100
1/2^2 + 1/3^2 +... + 1/100^2 < 3/4 - 1/100 < 3/4 (đpcm)
3A=3/1X4 + 3/4X7 + ...+3/298X301
3A=1/1-1/4+1/4-1/7+...+1/298-1/301
3A=1/1+(-1/4+1/4)+(-1/7+1/7)+...+(-1/298+1/298)-1/301
3A=1/1+0+0+0+0+0+...+0-1/301
3A=1/1-1/301
3A=301/301-1/301
3A=300/301
A=300/301:3
A=300/301X1/3
A=300/903
A=100/301
QUA CHI TIET
TICK VOI
A= 1/3 + 1/3^2 + ... + 1/3^8
3A= 3. (1/3+ 1/3^2+ ... + 1/3^8)
3A=1+ 1/3 + 1/3^2+ ... +1/3^7
=> 3A - A= (1 + 1/3 + 1/3^2 + ... + 1/3^7) - (1/3 + 1/3^2+ ... + 1/3^8)
=> 2A= 1 - 1/ 3^8
2A= 6560/6561
A= 6560/6561 : 2
A= 3280/6561
\(\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{4}\right)\left(1+\dfrac{1}{5}\right)+...+\left(1+\dfrac{1}{2021}\right)\)
= \(\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot\dfrac{6}{5}\cdot...\cdot\dfrac{2022}{2021}\)
= \(\dfrac{2022}{3}\)
Giải:
a)A=1/56+1/72+1/90+1/110+1/132+1/156
A=1/7.8+1/8.9+1/9.10+1/10.11+1/11.12+1/12.13
A=1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11-1/12+1/12-1/13
A=1/7-1/13
A=6/91
b)B=4/21+4/77+4/165+4/285+4/437+4/621
B=4/3.7+4/7.11+4/11.15+4/15.19+4/19.23+4/23.27
B=1/3-1/7+1/7-1/11+1/11-1/15+1/15-1/19+1/19-1/23+1/23-1/27
B=1/3-1/27
B=8/27
c) C=1/21+1/77+1/165+1/285+1/437+1/621
C=1/3.7+1/7.11+1/11.15+1/15.19+1/19.23+1/23.27
C=1/4.(4/3.7+4/7.11+4/11.15+4/15.19+4/19.23+4/23.27)
C=1/4.(1/3-1/7+1/7-1/11+1/11-1/15+1/15-1/19+1/19-1/23+1/23-1/27)
C=1/4.(1/3-1/27)
C=1/4.8/27
C=2/27
d) D=1/1.6+1/6.11+1/11.16+1/16.21+1/21.26+1/26.31
D=1/5.(5/1.6+5/6.11+5/11.16+5/16.21+5/21.26+5/26.31)
D=1/5.(1/1-1/6+1/6-1/11+1/11-1/16+1/16-1/21+1/21-1/26+1/26-1/31)
D=1/5.(1/1-1/31)
D=1/5.30/31
D=6/31
Nếu câu d cậu viết thiếu thì làm như vầy nhé!
Chúc bạn học tốt!
Nếu như câu d ko chép sai thì làm thế này nha:
d) D=1/1.6+1/6.11+1/11.16+1/16.21+1/26.31
D=1/5.(5/1.6+5/6.11+5/11.16+5/16.21)+1/806
D=1/5.(1/1-1/6+1/6-1/11+1/11-1/16+1/16-1/21)+1/806
D=1/5.(1/1-1/21)+1/806
D=1/5.20/21+1/806
D=4/21+1/806
D=3245/16926
Chúc bạn học tốt!
