\(12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(=\frac{1}{2}\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(=\frac{1}{2}\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(=\frac{1}{2}\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(=\frac{1}{2}\left(5^{32}-1\right)\left(5^{32}+1\right)\)

\(=\frac{1}{2}\left(5^{64}-1\right)\)

\(A=\left(5+1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(4A=\left(5-1\right)\left(5+1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(4A=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(4A=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

...

\(4A=5^{64}-1\)

\(\Rightarrow A=\frac{5^{64}-1}{4}>B=\frac{5^{64}-1}{5}\)

Ai trả lời đúng và nhanh nhất mik sẽ

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

B)A*2=(1/2+1/4+....+1/256)*2

=1+1/2+1/4+....+1/128)

A*2-A=(1+1/2+1/4+...+1/128)-(1/2+1/4+...+1/256)

=1-1/256

=255/256

a) Đặt A = \(\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}\)

  \(\Rightarrow\frac{1}{3}\times A=\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}+\frac{5}{486}\)

Lấy \(A-\frac{1}{3}\times A\)theo vế ta có : 

\(A-\frac{1}{3}\times A=\left(\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}\right)-\left(\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}+\frac{5}{486}\right)\)

\(\Rightarrow\frac{2}{3}\times A=\frac{5}{2}-\frac{5}{486}\)

\(\Rightarrow\frac{2}{3}\times A=\frac{605}{243}\)

  \(\Rightarrow A=\frac{605}{243}:\frac{2}{3}\)

  \(\Rightarrow A=\frac{605}{162}\)

Vậy  \(\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}=\frac{605}{162}\)

b) Đặt B = \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}+\frac{1}{256}\)

=> \(\frac{1}{2}\times B=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{256}+\frac{1}{512}\)

Lấy B trừ \(\frac{1}{2}\times B\)theo vế ta có : 

\(B-\frac{1}{2}\times B=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...++\frac{1}{128}+\frac{1}{256}\right)-\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+...+\frac{1}{512}\right)\)

\(\Rightarrow\frac{1}{2}\times B=\frac{1}{2}-\frac{1}{512}\)

\(\Rightarrow\frac{1}{2}\times B=\frac{255}{512}\)

\(\Rightarrow B=\frac{255}{512}:\frac{1}{2}\)

\(\Rightarrow B=\frac{255}{256}\)

Vậy \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{256}=\frac{255}{256}\)

cách giải bài này như nào: 5/20+1/4+6/24+8/32=bao nhiêu

    \(\dfrac{4}{5}\) : (\(\dfrac{4}{5}\) .- \(\dfrac{5}{4}\)) : (\(\dfrac{16}{25}\) - \(\dfrac{1}{5}\))

=  \(\dfrac{4}{5}\) : (-1) : (\(\dfrac{16}{25}\) - \(\dfrac{5}{25}\))

= -\(\dfrac{4}{5}\)  : \(\dfrac{11}{25}\)

= - \(\dfrac{4}{5}\) x \(\dfrac{25}{11}\)

=  - \(\dfrac{20}{11}\)

    \(\dfrac{11}{12}\) : (\(\dfrac{7}{9}\) + \(\dfrac{-1}{3}\)) - (\(\dfrac{2}{3}\) - \(\dfrac{5}{15}\))

= \(\dfrac{11}{12}\) : (\(\dfrac{7}{9}\) - \(\dfrac{3}{9}\)) - (\(\dfrac{2}{3}\) - \(\dfrac{1}{3}\))

= \(\dfrac{11}{12}\) : \(\dfrac{4}{9}\) - \(\dfrac{1}{3}\)

= \(\dfrac{11}{12}\) x \(\dfrac{9}{4}\) - \(\dfrac{1}{3}\)

= \(\dfrac{99}{48}\) - \(\dfrac{1}{3}\)

= \(\dfrac{99}{48}\) - \(\dfrac{16}{48}\)

= \(\dfrac{83}{48}\)  

\(\dfrac{4}{5}\): (\(\dfrac{4}{5}\).-\(\dfrac{5}{4}\)) : (\(\dfrac{16}{25}\) - \(\dfrac{1}{5}\))

=\(\dfrac{4}{5}\) x - 1: (\(\dfrac{16}{25}\) - \(\dfrac{5}{25}\))

= - \(\dfrac{4}{5}\) : \(\dfrac{11}{25}\)

= - \(\dfrac{4}{5}\) x \(\dfrac{25}{11}\)

= - \(\dfrac{20}{11}\) 

\(\dfrac{11}{12}\): (\(\dfrac{7}{9}\) + - \(\dfrac{1}{3}\)) - (\(\dfrac{2}{3}\) - \(\dfrac{5}{15}\))

= \(\dfrac{11}{12}\) : (\(\dfrac{7}{9}\) - \(\dfrac{3}{9}\)) - (\(\dfrac{2}{3}\) - \(\dfrac{1}{3}\))

= \(\dfrac{11}{12}\) : \(\dfrac{4}{9}\) - \(\dfrac{1}{3}\)

= \(\dfrac{11}{12}\) x \(\dfrac{9}{4}\) - \(\dfrac{1}{3}\)

= \(\dfrac{99}{48}\) - \(\dfrac{16}{48}\)

= \(\dfrac{83}{48}\) 

- \(\dfrac{2}{5}\).(\(\dfrac{9}{8}\) + \(\dfrac{16}{32}\) - \(\dfrac{3}{4}\)) - \(\dfrac{9}{10}\)

= - \(\dfrac{2}{5}\).(\(\dfrac{9}{8}\) + \(\dfrac{4}{8}\) - \(\dfrac{6}{8}\)) - \(\dfrac{9}{10}\)

= - \(\dfrac{2}{5}\).(\(\dfrac{13}{8}\) - \(\dfrac{6}{8}\)) - \(\dfrac{9}{10}\)

= - \(\dfrac{2}{5}\).\(\dfrac{7}{8}\) - \(\dfrac{9}{10}\)

= - \(\dfrac{7}{20}\) - \(\dfrac{18}{20}\)

= - \(\dfrac{5}{4}\)

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

Trả lời cái kiểu gì thế 

lớp 4 mà khó như lớp 5 phét vừa thôi ông nha

Lời giải:

$A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}$

$2\times A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}$

$2\times A-A=(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32})-(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64})$

$A=1-\frac{1}{64}=\frac{63}{64}$

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

 2A = 2.(1/2+1/4+1/8+1/16+1/32+1/64)
            = 1 + 1/2+1/4+1/8+1/16+1/32
=> 2A - A = (1+1/2+1/4+1/8+1/16+1/32) - (1/2+1/4+1/8+1/16+1/32+1/64)
=> A = 1 - 1/64
         = 63/64