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-1-1/2-1/4-1/8......-1/1024
=-(1+1/2+1/4+1/8...+1/1024)
mà ta có 1024=2^10
nên -(1+1/2+1/4+1/8...+1/1024)
=-(2^9+2^8+2^7....+1)/2^10
=-(1023/1024)
=-1,99.........
mình sẽ làm lại bai này cho đúng nha
\(-1-\frac{1}{2}-\frac{1}{4}....-\frac{1}{1024}=-1-\left(\frac{1}{2}+\frac{1}{4}+...\frac{1}{1024}\right)\)
\(=-1-\left(\frac{1}{2^1}+\frac{1}{2^2}...+\frac{1}{2^{10}}\right)\)
\(=-1-\frac{1023}{1024}=\frac{-1024}{1024}-\frac{1023}{1024}=\frac{-2047}{1024}\)
vậy mới đúng nha
ta có\(\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-...-\frac{1}{1024}\)
\(=\frac{1}{2}-\left(\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)\)
tách
\(B=\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\)
\(2B=\frac{1}{2}+\frac{1}{4}+...+\frac{1}{512}\)
\(2B-B=\frac{1}{2}-\frac{1}{1024}\)
thay vào B ta có
\(\frac{1}{2}-\left(\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)\)
\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{1024}=\frac{1}{1024}\)
\(A=\frac{1}{2}-\frac{1}{4}-\cdot\cdot\cdot-\frac{1}{1024}\)
\(\Rightarrow A=\frac{1}{2}-\frac{1}{2^2}-\cdot\cdot\cdot-\frac{1}{2^{10}}\)
\(\Rightarrow2A=1-\frac{1}{2}-\cdot\cdot\cdot-\frac{1}{2^9}\)
\(\Rightarrow2A-A=\left(1-\frac{1}{2}-\cdot\cdot\cdot-\frac{1}{2^9}\right)-\left(\frac{1}{2}-\frac{1}{2^2}-\cdot\cdot\cdot-\frac{1}{2^{10}}\right)\)
\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2^{10}}\)
\(\Rightarrow A=\frac{1}{2}+\frac{1}{2^{10}}\)
\(\Rightarrow A=\frac{2^9+1}{2^{10}}\)
\(\Rightarrow A=\frac{513}{1024}\)
Đặt \(A=-1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-...-\frac{1}{2014}\)
\(\Rightarrow-A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\)
\(-A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)
\(\Rightarrow-2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)
\(\Rightarrow-2A-\left(-A\right)=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^9}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{10}}\right)\)
\(-A=2-\frac{1}{2^{10}}\)
\(\Rightarrow A=\frac{1}{2^{10}}-2\)
\(\dfrac{8^2.4^5}{2^{20}}\) = \(\dfrac{\left(2^3\right)^2\left(2^2\right)^5}{2^{20}}\) = \(\dfrac{2^6.2^{10}}{2^{20}}\) = \(\dfrac{2^{16}}{2^{20}}\) = \(\dfrac{1}{2^4}\) = \(\dfrac{1}{16}\)
\(A,\)\(A=\left(3998+3997+4005\right)\)\(+\left(4004+4006\right)-10\)
\(A=12000+8010-10=12000+\)\(8000=20000\)
\(B,\)\(B=625\times32\times24\times250\)
\(B=\left[\left(25\times25\right)\times\left(4\times4\times2\right)\right]\times\)\(\left(4\times6\right)\times250\)
\(B=\left(25\times4\right)\times\left(25\times4\right)\times2\times6\times\left(4\times250\right)\)
\(B=100\times100\times12\times1000=120000000\)
\(C,\)\(C=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\)
\(\Rightarrow2C=\frac{2}{2}+\frac{2}{4}+\frac{2}{8}+...+\frac{2}{1024}\)\(=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{512}\)
\(\Rightarrow2C-C=\)\(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{512}-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)\)
\(\Rightarrow C=1-\frac{1}{1024}=\frac{1023}{1024}\). Mình làm thế cho chi tiết thôi còn để thế nào thì tùy bạn nhé.
Chúc bạn hok tốt :)
A = 1/2 - 1/4 - 1/8 -...- 1/512 - 1/1024
2A = 2(1/2 - 1/4 - 1/8 -...- 1/512 - 1/1024)
2A = 1 - 1/2 - 1/8 -...- 1/1024 - 1/2048
2A - A = 1 - 1/2 - 1/8 -....- 1/1024 - 1/2048 - (1/2 - 1/4 - 1/8 - ...- 1/512 - 1/1024)
A = 1 - 1/2048
A = 2047/2048
Em mới học lớp 6, vậy anh thua em rồi. HIHI
mk làm toán thôi
2x=5y =>x/5=y/2
đặt x/5=y/2=k =>x=5k;y=2k
thay vào x2+y2=116
(5k)^2+(2k)^2=116
25.k^2+4.k^2=116
(25+4)k^2=116
k^2=116/29=4
=>k=2 hoặc k=-2
xét k=2 và k=-2
Đặt
\(S=1+2+4+...+2048+4096\)
\(S=1+2^1+2^2+...+2^{11}+2^{12}\)
\(2S=2+2^2+2^3+...+2^{12}+2^{13}\)
\(2S-S=\left(2+2^2+2^3+...+2^{13}\right)-\left(1+2+2^2+..+2^{12}\right)\)
\(S=2^{13}-1=8192-1=8191\)
Gọi A=1+2+4+8+16+...+1024+2048+4096
2A=2+4+8+16+32+...+2048+4096+8192
2A-A=(2+4+8+16+32+...+2048+4096+8192)-(1+2+4+8+16+...+1024+2048+4096)
A=8192-1
A=8191