b: A=1/3+1/9+...+1/3^10

=>3A=1+1/3+...+1/3^9

=>A*2=1-1/3^10=(3^10-1)/3^10

=>A=(3^10-1)/(2*3^10)

c: C=3/2+3/8+3/32+3/128+3/512

=>4C=6+3/2+...+3/128

=>3C=6-3/512

=>C=1023/512

d: A=1/2+...+1/256

=>2A=1+1/2+...+1/128

=>A=1-1/256=255/256

\(1+\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)

\(=\frac{64}{64}+\frac{80}{64}+\frac{40}{64}+\frac{20}{64}+\frac{10}{64}+\frac{5}{64}\)

\(=\frac{64+80+40+20+10+5}{64}\)

\(=\frac{219}{64}\)

\(=\frac{27}{8}\)

1+5/4+5/8+5/16+5/32+5/64

=1+5/4+5/8+5/16+5/32+5/64

=1+(5/4+5/8+5/16+5/32+5/64)

=1+[5x(1/4+1/8+1/16+1/32+1/64)]

A=1/4+1/8+1/16+1/32+1/64

2A=1/2+1/4+1/8+1/16+1/32

2A-A=(1/2+1/4+1/8+1/16+1/32)+(1/4+1/8+1/16+1/32+1/64)

A=1/2-1/64

A=31/64

1+[5x31/64]

=1+155/64

=219/64

Đặt \(A=\frac54+\frac58+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)

=>\(A\times2=\frac52+\frac54+\frac58+\frac{5}{16}+\frac{5}{32}\)

=>\(2\times A-A=\frac52+\frac54+\frac58+\frac{5}{16}+\frac{5}{32}-\frac54-\frac58-\frac{5}{16}-\frac{5}{32}-\frac{5}{64}\)

=>\(A=\frac52-\frac{5}{64}=\frac{160}{64}-\frac{5}{64}=\frac{155}{64}\)

Ta có: \(1+\frac54+\frac58+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)

\(=1+\frac{155}{64}=\frac{64+155}{64}=\frac{219}{64}\)

1 + 5/4 + 5/8 + 5/32 + 5/64 = 37/64 = 199/ 64

Đây bạn nhé!

\(E=\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)

\(\Leftrightarrow E=\frac{5}{2^2}+\frac{5}{2^3}+\frac{5}{2^4}+\frac{5}{2^5}+\frac{5}{2^6}\)

\(\Leftrightarrow E=5\left(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\right)\)

Đặt \(A=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\)

\(\Rightarrow2A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}\)

\(\Rightarrow2A-A=\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}\right)-\left(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\right)\)

\(\Rightarrow A=\frac{1}{2}-\frac{1}{2^6}\)

Thay \(A=\frac{1}{2}-\frac{1}{2^7}\)vào E ta được:

\(E=5\cdot\left(\frac{1}{2}-\frac{1}{2^6}\right)\)

Bài làm

~ Đề là tính E, mà làm theo cách của bạn Vũ Hà My đây thì nó lại vừa dài, vừa khó ra kết quả. Nên mik sẽ làm theo cách quy đồng nhé. Dấu " . " là dấu nhân nha.  ~

\(E=\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)

\(E=5.\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)

\(E=5.\left(\frac{16}{64}+\frac{8}{64}+\frac{4}{64}+\frac{2}{32}+\frac{1}{64}\right)\)

\(E=5.\frac{31}{64}\)

\(E=\frac{155}{64}\)

Vậy \(E=\frac{155}{64}\)

TRA LOI:

1+5/4+5/8+5/16+5/32+5/64=219/64

3+3/5+3/25+3/125+3/512=3,8

các bạn giải khó hiểu quá tui mới học lớp 5 mà

5/2 + 5/4 + 5/8 + 5/16 + 5/32 + 5/64 

= 5(1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)

Đặt A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64

=> 2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32

=> 2A - A = 1 - 1/64

=> A = 1 - 1/64

Do đó : 5(1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64) = 5(1 - 1/64) = 5 . 63/64 = 315/64 

nhanh len gium minh duoc ko

a)    \(A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)

\(=1+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}\)

\(\Rightarrow\)\(2A=2+1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\)

\(\Rightarrow\)\(2A-A=\left(2+1+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^6}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^7}\right)\)

\(\Leftrightarrow\)\(A=2-\frac{1}{2^7}=\frac{255}{128}\)

b)  \(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\)

\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{21}\right)\)

\(=\frac{1}{2}.\frac{2}{7}=\frac{1}{7}\)