a,1 + 1/5 + 1/25 + 1/125 + 1/625
b,1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96
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a) = \(\frac{127}{96}\)
b) = \(\frac{255}{256}\)
c) Mik bỏ nha
d) = \(\frac{1023}{512}\)
e) = \(\frac{2343}{625}\)
1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96 + 1/192
= 127/192
k minh di , xin day
\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}+\frac{1}{768}+\frac{1}{1536}\)
\(A\times2=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{96}+\frac{2}{192}+\frac{2}{384}+\frac{2}{768}+\frac{2}{1536}\)
Rút gọn ta được
\(A\times2=\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}+\frac{1}{768}\)
\(A\times2-A=\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{768}-\left[\frac{1}{3}+\frac{1}{6}+...+\frac{1}{1536}\right]\)
\(A=\frac{2}{3}+\frac{1}{3}-\frac{1}{3}-\frac{1}{1536}\)
\(A=\frac{2}{3}-\frac{1}{1536}=\frac{341}{512}\)
A= 1/3+1/6+1/12+1/24+1/48+1/96
= (1/3+1/6)+(1/12+1/24)+(1/48+1/96)
= (2/6+1/6)+(2/24+1/24)+(2/96+1/96)
= 1/2+1/8+1/32
= 16/32+4/32+1/32
= 21/32
Vậy A=21/32
Giải:
A=1/3+1/6+1/12+1/24+1/48+1/96
A=1/3+(1/2.3+1/3.4)+(1/4.6+1/6.8)+1/96
A=1/3+(1/2-1/3+1/3-1/4)+[1/2.(2/4.6+2/6.8)]+1/96
A=1/3+(1/2-1/4)+[1/2.(1/4-1/6+1/6-1/8)]+1/96
A=1/3+1/4+[1/2.(1/4-1/8)]+1/96
A=1/3+1/4+[1/2.1/8]+1/96
A=1/3+1/4+1/16+1/96
A=7/12+7/96
A=21/32
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}=\frac{21}{32}\)
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1/3 + 1/6+1/12+1/24+1/48+1/96
= 2/3 – 1/3 + 1/3 – 1/6+1/6- 1/12+1/12- 1/24+1/24-
1/48+1/48-1/96
=2/3_1/96
= 63/96
= 21/32
= 1-1/3+1/3-1/6+1/6-1/12+1/12-1/24+1/24-1/48+1/48-1/96+1/96-1/192
= 1-1/192 = 191 / 192