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= 128/256 + 64/256 + 32/256 + 16/256 + 8/256 + 4/256 + 2/256 + 1/256
= 255/256
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{100}-\frac{1}{200}+\frac{1}{200}-\frac{1}{400}\)
\(A=1-\frac{1}{400}\)
\(A=\frac{399}{400}\)
A= 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
2A= 2(1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256)
= 1+1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128
=>A = 2A-A =1+1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 -1/2 - 1/4 - 1/8 - 1/16 - 1/32 - 1/64 - 1/128 - 1/256
=1-1/256
=255/256
tính nhanh hộ mình câu này nha (có kèm bài làm , ai nhanh mình tick cho );
1/2+1/4+1/8+1/16+1/32+1/64
(1/2+1/8)+(1/4+1/16)+(1/8+1/32)+1/64
=1/10+1/20+1/40+1/64
=61/320
lấy 1/64 làm mẫu xố chung
1/64+2/64+4/64+8/64+12/64+32/64=59/64
1/2 : 0,5 - 1/4 : 0,25 - 1/8 - 0,125 : 1/10 - 0,1 = 1/2 : 1/2 - 1/4 : 1/4 - 1/8 - 1/8 : 1/10 - 1/10 .
= 1 - 1 - 1/8 - 1/10 : ( 1/8 - 1 ) .
= 0 - 1/8 - 1/10 : ( -7/8 ) .
= -7/8 - 1/10 : ( -7/8 ) .
= -7/8 : ( 1 - 1/10 ) .
= -7/8 : 9/10 .
= -7/8 . 10/9 .
= -35/36 .
1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
= 1/2 - 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + ... + 1/256 - 1/512
= 1/2 - 1/512
= 255/512
Gọi \(\frac{1}{4}+\frac{1}{8}+\frac{1}{6}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\) là A
Ta có :
\(A=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\)
\(2A=2.\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\right)\)
\(2A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)
\(2A-A=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\right)-\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{11}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\right)\)
\(A=\frac{1}{2}-\frac{1}{512}\)
\(A=\frac{255}{512}\)
Vậy ..........
\(ĐặtA=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)
\(A=1-\frac{1}{64}=\frac{63}{64}\)
bn tham khảo link này nha:
https://olm.vn/hoi-dap/detail/1930834278.html
k nha
học tốt# mui #