Tính nhanh A=1/3+1/3^2+1/3^3...+1/3^8
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HT
11 tháng 8 2015
A = \(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
3A = \(1+3+\frac{1}{3^2}+...+\frac{1}{3^7}\)
2A = 3A - A = \(1-\frac{1}{3^8}\)
=> A = \(\frac{1-\frac{1}{3^8}}{2}\)
ML
11 tháng 8 2015
\(A=\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^8}\)
=>3A=\(1+\frac{1}{3}+...+\frac{1}{3^7}\)
=>3A-A=\(\left(1+\frac{1}{3}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^8}\right)\)
=>2A=\(1-\frac{1}{3^8}=\frac{3^8-1}{3^8}\)
=>A=\(\frac{3^8-1}{3^8}:2=\frac{3^8-1}{2.3^8}\)
MT
12 tháng 8 2015
A=1/3+1/32+1/33+...+1/38
=>3A=1+1/3+1/32+...+1/37
=>3A-A=(1+1/3+1/32+...+1/37)-(1/3+1/32+1/33+...+1/38)
=>2A=1+1/3+1/32+...+1/37-1/3-1/32-1/33-...-1/38
=1-1/38
=\(\frac{6550}{6561}\)
=>A=\(\frac{6560}{6561}:2=\frac{6560}{6561}.\frac{1}{2}=\frac{3280}{6561}\)
3 tháng 3 2019
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
4 tháng 5 2015
\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+........+\frac{1}{3^8}\)
\(3A=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+..........+\frac{1}{3^7}\)
\(3A-A=1-\frac{1}{3^8}\)
\(A=\left(1-\frac{1}{3^8}\right):2\)
CR
1
8 tháng 8 2017
\(A=1+3+3^2+3^3+3^4\)
\(A=1+3+9+27+81\)
\(A=121\)
\(B=\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\)
\(8B=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\)
\(8B=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\)
\(8B=\left(3^8-1\right)\left(3^8+1\right)\)
\(8B=3^{16}-1\)
\(B=\frac{1}{8}\left(3^{16}-1\right)\)
\(B=\frac{3^{16}}{8}-\frac{1}{8}\)
\(B=\text{ }\frac{43046721}{8}-\frac{1}{8}\)
\(B=\frac{43046720}{8}\)
\(B=5380840\)
HT
2
7 tháng 3 2023
a. \(\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\dfrac{3}{4}=1+\dfrac{3}{4}=\dfrac{7}{4}\)
b. \(\dfrac{3}{4}+\dfrac{3}{5}+\dfrac{2}{8}+\dfrac{4}{10}=\left(\dfrac{3}{4}+\dfrac{2}{8}\right)+\left(\dfrac{3}{5}+\dfrac{4}{10}\right)=1+1=2\)
7 tháng 3 2023
a ) `1/3 + 3/4 + 2/3 + 1/4 `
`= (1/3 + 2/3 )+ (3/4 + 1/4)`
`= 1 + 1 `
`= 2
b 3/4 + 3/5 + 2 phần 8 + 4/10`
`= (3/4 + 2/8 ) + ( 3/5 + 4/10 ) `
`= 1 + 1 `
`= 2`
25 tháng 9 2020
a.
\(\left(1\frac{1}{4}+\frac{3}{5}\right):\left(-\frac{11}{12}\right)+\left(\frac{3}{8}-1\frac{2}{5}\right):\left(-\frac{11}{12}\right)\)
\(=\left(\frac{5}{4}+\frac{3}{5}+\frac{3}{8}-\frac{7}{5}\right):\left(-\frac{11}{12}\right)\)
\(=\left(\frac{13}{8}-\frac{4}{5}\right):\left(-\frac{11}{12}\right)\)
\(=\frac{33}{40}:\left(-\frac{11}{12}\right)\)
\(=\frac{33}{40}\cdot\left(-\frac{12}{11}\right)\)
\(=\frac{-9}{10}\)
b.
\(\left(\frac{3}{8}-1\frac{2}{5}\right):\left(-\frac{11}{15}\right)+\left(1\frac{1}{4}+\frac{3}{5}\right):\left(-\frac{11}{15}\right)\)
\(=\left(\frac{3}{8}-\frac{7}{5}+\frac{5}{4}+\frac{3}{5}\right):\left(-\frac{11}{15}\right)\)
\(=\left(\frac{13}{8}-\frac{4}{5}\right):\left(-\frac{11}{15}\right)\)
\(=\frac{33}{40}:\left(-\frac{11}{15}\right)\)
\(=\frac{33}{40}\cdot\left(-\frac{15}{11}\right)\)
\(=\frac{-9}{8}\)
Ta có: \(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\)
\(\Rightarrow3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\right)\)
\(\Rightarrow2A=1-\frac{1}{3^8}\)
\(\Rightarrow A=\left(1-\frac{1}{3^8}\right)\div2\)
\(\Rightarrow A=\frac{1}{2}-\frac{1}{3^8\times2}\)
A=1/3+1/3^2+1/3^3+...+1/3^8
3A=1+1/3+1/3^2+...+1/3^7
3A-A=1-1/3+1/3-1/3^2+1/3^2-1/3^3+...+1/3^7-1/3^8
2A=1-1/3^8
2A=6560/6561
Suy ra A=3280/6561
nho k cho minh voi nhe