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\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}+\frac{1}{768}+\frac{1}{1536}\)
\(A\times2=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{96}+\frac{2}{192}+\frac{2}{384}+\frac{2}{768}+\frac{2}{1536}\)
Rút gọn ta được
\(A\times2=\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}+\frac{1}{768}\)
\(A\times2-A=\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{768}-\left[\frac{1}{3}+\frac{1}{6}+...+\frac{1}{1536}\right]\)
\(A=\frac{2}{3}+\frac{1}{3}-\frac{1}{3}-\frac{1}{1536}\)
\(A=\frac{2}{3}-\frac{1}{1536}=\frac{341}{512}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\)
\(=\frac{2-1}{1\cdot2}+\frac{3-2}{2\cdot3}+...+\frac{6-7}{6\cdot7}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}\)
\(=1-\frac{1}{7}\)
\(=\frac{6}{7}\)
1-2+3-4+5-6+......+101-102+103
\(\left(1-2\right)+\left(3-4\right)+\left(5-6\right)+...+\left(101-102\right)+103\)
\(\left(-1\right)+\left(-1\right)+\left(-1\right)+...+\left(-1\right)+103\)( có 51 cặp số (1) )
\(\left(-51\right)+103\)
\(52\)
Vậy ...
1-2+3-4+5-6+......+101-102+103
=(103 - 102)+(101 - 100)+...+(7 - 6)+(5 - 4)+(3 - 2)+1
Ta thấy dãy trên có 51 cặp , mỗi cặp đều có tổng bằng 1.
= 1 * 51 +1
=1 * 52
=52.
xin lỗi mk viết thiếu => 3A-A= 19683-1
=> 2A=19683-1
=> A= (19683-1) :2
= 9841
A = 1 + 3 + 9 + 27 + ... + 2187
A x 3 = 1 x 3 + 3 x 3 + ... + 2187 x 3
A x 3 = 3 + 9 + ... + 6561
A = 6561 - 3 = 6558
( 1/2 + 1/6 + 1/12 + 1/30 ) : ( 1/3 + 1/6 + 1/12 + 1/ 24 + 1/48 )=(1/1.2 + 1/2.3 + 1/3.4 +1/5.6 ):(1/3.1 +1/3.2 + 1/3.4 + 1/3.8 +1/3.16)=....
\(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{30}\right):\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}\right)\)
\(=\left(\frac{12}{12}+\frac{2}{12}+\frac{1}{12}+\frac{1}{30}\right):\left(\frac{16}{16}+\frac{8}{48}+\frac{4}{48}+\frac{2}{48}+\frac{1}{48}\right)\)
\(=\left(\frac{15}{12}+\frac{1}{30}\right):\frac{31}{48}\)
\(=\left(\frac{225}{180}+\frac{6}{180}\right):\frac{31}{48}\)
\(=\frac{231}{180}:\frac{31}{48}\)
\(=\frac{231}{180}.\frac{48}{31}=\frac{231.24}{90.31}\)
\(=\frac{5544}{2790}\)nếu rút gọn được thì bạn rút gon luôn nhé
A = 3 + 6 + 12 +24 + ... + 768 + 1536
A x 2 = 6 + 12 + 24 + 48 + ... + 1536 + 3072
A = 3 + 3072 = 3075
chịu nha bạn