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\(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{12}{15}+\frac{22}{33}+\frac{48}{64}\)
\(=\frac{11}{33}+\frac{16}{64}+\frac{3}{15}+\frac{12}{15}+\frac{22}{33}+\frac{48}{64}\)
\(=\left(\frac{11}{33}+\frac{22}{33}\right)+\left(\frac{16}{64}+\frac{48}{64}\right)+\left(\frac{3}{15}+\frac{12}{15}\right)\)
\(\frac{33}{33}+\frac{64}{64}+\frac{15}{15}\)
\(=1+1+1\)
\(=3\)
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
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
Tính nhanh:
\(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\)\(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\)
\(=\left(\frac{1}{1}+\frac{1}{9}\right)+\left(\frac{1}{2}+\frac{1}{8}\right)\)\(+\left(\frac{1}{3}+\frac{1}{7}\right)+\left(\frac{1}{4}+\frac{1}{6}\right)+\frac{1}{5}\)
\(=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{5}\)
\(=\frac{4}{10}+\frac{2}{5}=\frac{2}{5}+\frac{1}{5}=\frac{3}{5}\)
tks giúp mk nha! cảm ơn nhiều ạ...
Đặt \(A=2-1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)
\(=2-\frac{1}{9}=\frac{18}{9}-\frac{1}{9}=\frac{17}{9}\)
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!!!!!
ta có : A=1/2+1/4+..+1/1024
=> A=1/21+1/22+..+1/210
=> A.2=(1/21+1/22+..+1/210).2
=> A.2=1+1/21+1/22+..+1/29
=> 2A-A=(1+1/21+1/22+..+1/29)-(1/21+1/22+..+1/210)
=> A=1-1/210