1/3+1/6+1/12+...........+1/1536+1/3072
Tính nhanh :
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{1536}+\frac{1}{3072}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{1536}+\frac{1}{3072}\)
\(=\frac{2}{3}-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{12}+\frac{1}{12}-\frac{1}{24}+...+\frac{1}{1536}-\frac{1}{3072}\)
\(=\frac{2}{3}+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{6}-\frac{1}{6}\right)+\left(\frac{1}{12}-\frac{1}{12}\right)+...+\left(\frac{1}{1536}-\frac{1}{1536}\right)-\frac{1}{3072}\)
\(=\frac{2}{3}-\frac{1}{3072}\)
\(=\frac{2047}{3072}\)
1 + 1 + 1 +....................+ 1 + 1
3 6 12 1536 3072
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1/3+1/6+1/12+1/24+....+1/768+1/1536
1/3+1/6+1/12+1/24+....+1/768+1/1536
\(A=\dfrac{1}{3}\left(1+\dfrac{1}{2}+...+\dfrac{1}{256}+\dfrac{1}{512}\right)\)
Đặt B=1+1/2+...+1/256+1/512
=>2B=2+1+...+1/128+1/256
=>B=2-1/512=1023/512
=>\(A=\dfrac{1}{3}\cdot\dfrac{1023}{512}=\dfrac{341}{512}\)
ting gia tri bieu thuc
A =1/3+1/6+1/12+...+1/1536+1/3072 B=4/3*5+4/5*7+4/7*9+...+4/2007*2009
tính giá trị biểu thức :
A =1/3+1/6+1/12+...+1/1536+1/3072 B=4/3*5+4/5*7+4/7*9+...+4/2007*2009
B = 4/3*5 +4/5*7+4/7*9+.....+4/2007*2009
B x2 =4/3*5 + 4/5*7 + 4/7*9 + .,...+4/2007+2009
B x2 =4/3 - 4/5 + 4/5 -4/7 + 4/7 -4/9 + 4/9 + ......+4/2007 - 4/2009
B x2=4/3 -4/2009
Bx2=1,331342293
B =1,331342293 : 2
B =4012/6027
a=1/3 + 1/6 +1/12 +.....+ 1/1536 +1/3072
a=2/3 - 1/3 + 1/3 - 1/6 +1/6 -1/12 + ....- 1/1536 +1/3072
a=2/3 - 1/3072
a=2047/3072
A=1/3 + 1/6 + 1/12 +1/24 + ............+ 1/768 + 1/1536
A = 1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96 + 1/192 + 1/384 + 1/768 +1/1536
\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}+\frac{1}{768}+\frac{1}{1536}\)
\(A\times2=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{96}+\frac{2}{192}+\frac{2}{384}+\frac{2}{768}+\frac{2}{1536}\)
Rút gọn ta được
\(A\times2=\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}+\frac{1}{768}\)
\(A\times2-A=\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{768}-\left[\frac{1}{3}+\frac{1}{6}+...+\frac{1}{1536}\right]\)
\(A=\frac{2}{3}+\frac{1}{3}-\frac{1}{3}-\frac{1}{1536}\)
\(A=\frac{2}{3}-\frac{1}{1536}=\frac{341}{512}\)
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tính nhanh: 1+2+3+6+12+....+3072