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\(M=\frac{1}{1000}+\frac{13}{1000}+\frac{25}{1000}+\frac{37}{1000}+...+\frac{121}{1000}+\frac{133}{1000}\)
\(=\frac{1+13+25+37+...+121+133}{1000}\)
\(=\frac{804}{1000}=\frac{201}{250}\)
Đăt A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
Ta có : A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
2A = 1 + 1/2 + 1/4 + 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
2A = 1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512 - 1/512
2 A = 1 + ( 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512 ) - 1/512
2A = 1 + A - 1/512
2A - A = 1 - 1/512
A = 511 / 512
2A=1+1/2+1/4+1/8+.........+1/512
2A-A=(1+1/2+1/4+1/8+....+1/512)-(1/2+1/4+1/8+.....+1/1024)
A=1-1/1024
A=1023/1024
vậy A=1023/1024
A = (1/2+1/64)+(1/4+1/128)+(1/8+1/256)+(1/16+1/512)+(1/32+1/1024)
= 1/2(1+1/32)+1/4(1+1/32)+1/8(1+1/32)+1/16(1+1/32)+1/32(1+1/32)
= (1+1/32) x (1/2+/14+1/8+1/16+1/32)
= (33/32) x (31/32) = 1023/1024
\(\frac{1999x1999}{1995x1995_{ }}=\frac{1999^2}{1995^2}=\left(\frac{1999}{1995}\right)^2\)\(>1^2\)\(=1\)
A = 1/2 + 1/4 + 1/8 + ... + 1/1024
2A = 1 + 1/2 + 1/4 + ... + 1/512
2A - A = (1 + 1/2 + 1/4 + ... + 1/512) - (1/2 + 1/4 + 1/8 + ... + 1/1024)
A = 1 - 1/1024
A = 1023/1024
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{1024}\)
\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{4}+......+\frac{1}{512}\)
\(\Rightarrow A=2A-A=1-\frac{1}{1024}\)
\(A=\frac{1023}{1024}\)
Bài làm:
Xét: \(101\times102-101\times101-50-51=101\times\left(102-101\right)-101=101\times1-101=0\)
\(\Rightarrow\left(1+2+4+8+...+512\right)\times\left(101\times102-101\times101-50-51\right)=0\)
\(\Rightarrow\frac{\left(1+2+4+8+...+512\right)\times\left(101\times102-101\times101-50-51\right)}{2+4+8+16+...+1024+2048}=0\)
Học tốt!!!!
đề phải là 1 +1/2 + 1/4 +1/32 + 1/64 + 1/128 +1/256 +/512 +1/1024 moi dug
Mình nghĩ đây là nâng cao tiểu học
Đặt S = 1/2 + 1/4 + 1/8 + 1/16 + ...
==> 2S = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ...
2S = 1 + S
==> S = 1
Đây cũng là kết quả khi tính theo cấp số nhân khi n --> vô cùng
2A=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512
2A-A=1-1/1024
A=1-1/1024
A=1023/1024