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b) 1/3+1/3^2+1/3^3+1/3^4+1/3^5 (goi tong bang M)
3M=1+1/3+1/3^2+1/3^3+1/3^4
3M-M=1-1/3^5
2M=242/243
M=242/243*1/2=121/243
\(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
=\(1+\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}+\frac{1}{3^6}\)
=\(\frac{3^6}{3^6}+\frac{3^5}{3^6}+\frac{3^4}{3^6}+\frac{3^3}{3^6}+\frac{3^2}{3^6}+\frac{3^1}{3^6}+\frac{3^0}{3^6}\)
=\(\frac{3^6+3^5+3^4+3^3+3^2+3+1}{3^6}\)
=\(\frac{729+243+81+27+9+3}{729}\)
=\(\frac{1093}{729}\)
nha.
3636/4545+x=4848/1515
x=4848/1515-3636/4545
x=14544/4545-3636/4545
x=10908/4545
3535/5050-x=8/25
x=3535/5050-1616/5050
x=1919/5050
Ta có :
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2013.2014}\)
\(=\)\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}\)
\(=\)\(1-\frac{1}{2014}\)
\(=\)\(\frac{2014}{2014}-\frac{1}{2014}\)
\(=\)\(\frac{2013}{2014}\)
Vậy \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2013.2014}=\frac{2013}{2014}\)
Dấu \(.\) là dấu nhân nhé
Chúc bạn học tốt ~
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{2013\times2014}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}\)
\(=1-\frac{1}{2014}\)
\(=\frac{2013}{2014}\)
CHÚC BN HỌC TỐT!!!!!
\(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
\(=\frac{729}{729}+\frac{243}{729}+\frac{81}{729}+\frac{27}{729}+\frac{9}{729}+\frac{3}{729}+\frac{1}{729}\)
\(=\frac{729+243+81+27+9+3+1}{729}\)
\(=\frac{1093}{729}\)
gọi biểu thức trên là A
ta có : A = \(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\) (1)
\(\frac{1}{3}\)x A =\(\frac{1}{3}\)+\(\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}+\frac{1}{2187}\) (2)
lấy (1) - (2)
\(\frac{2}{3}xA\)= 1 - \(\frac{1}{2187}\)
\(\frac{2}{3}xA\)= \(\frac{2186}{2187}\)
A = \(\frac{2186}{2187}:\frac{2}{3}\)
A = \(\frac{1093}{729}\)
\(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{12}{15}+\frac{22}{33}+\frac{48}{64}\)
\(=\frac{11}{33}+\frac{16}{64}+\frac{3}{15}+\frac{12}{15}+\frac{22}{33}+\frac{48}{64}\)
\(=\left(\frac{11}{33}+\frac{22}{33}\right)+\left(\frac{16}{64}+\frac{48}{64}\right)+\left(\frac{3}{15}+\frac{12}{15}\right)\)
\(\frac{33}{33}+\frac{64}{64}+\frac{15}{15}\)
\(=1+1+1\)
\(=3\)
2186/729 nha bn k mk đi
A=1+1/3+1/9+...+1/729
3A=3+1+1/3+....+1/243
3A-A=(3+1+1/3+...+1/243)-(1+1/3+1/9+...+1/729)
2A=3-1/729
A=(3-1/729)/2
k cho mình nha