-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,3998 +3997+4004+4005+4006-10=20000

B,625x32x34x250=170000000

\(A,\)\(A=\left(3998+3997+4005\right)\)\(+\left(4004+4006\right)-10\)

\(A=12000+8010-10=12000+\)\(8000=20000\)

\(B,\)\(B=625\times32\times24\times250\)

\(B=\left[\left(25\times25\right)\times\left(4\times4\times2\right)\right]\times\)\(\left(4\times6\right)\times250\)

\(B=\left(25\times4\right)\times\left(25\times4\right)\times2\times6\times\left(4\times250\right)\)

\(B=100\times100\times12\times1000=120000000\)

\(C,\)\(C=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\)

\(\Rightarrow2C=\frac{2}{2}+\frac{2}{4}+\frac{2}{8}+...+\frac{2}{1024}\)\(=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{512}\)

\(\Rightarrow2C-C=\)\(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{512}-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)\)

\(\Rightarrow C=1-\frac{1}{1024}=\frac{1023}{1024}\). 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

kb nhé

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