X*3069=3069

X=3069/3069

X-1

X = 3069/3069

X = 1

k cho minh nha

1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96 + 1/192 + 1/384 = 85/128

0.6640625

85/128 nha 

a: \(A=1+\frac15+\frac{1}{25}+\cdots+\frac{1}{78125}\)

=>\(A=1+\frac15+\frac{1}{5^2}+\cdots+\frac{1}{5^7}\)

=>\(5\times A=5+1+\frac15+\cdots+\frac{1}{5^6}\)

=>\(5\times A-A=5+1+\frac15+\cdots+\frac{1}{5^6}-1-\frac15-\cdots-\frac{1}{5^7}\)

=>\(4\times A=5-\frac{1}{5^7}=\frac{5^8-1}{5^7}\)

=>\(A=\frac{5^8-1}{4\times5^7}\)

b:Sửa đề: \(B=\frac13+\frac{1}{12}+\cdots+\frac{1}{49152}\)

=>\(B=\frac13+\frac{1}{3\times4}+\frac{1}{3\times4^2}+\cdots+\frac{1}{3\times4^7}\)

=>\(4\times B=\frac43+\frac13+\frac{1}{3\times4}+\cdots+\frac{1}{3\times4^6}\)

=>\(4\times B-B=\frac43+\frac13+\frac{1}{3\times4}+\cdots+\frac{1}{3\times4^6}-\frac13-\frac{1}{3\times4}-\frac{1}{3\times4^2}-\cdots-\frac{1}{3\times4^7}\)

=>\(3\times B=\frac43-\frac{1}{3\times4^7}=\frac{4^8-1}{3\times4^7}\)

=>\(B=\frac{4^8-1}{9\times4^7}\)

c: \(C=\frac53+\frac56+\frac{5}{12}+\frac{5}{24}+\cdots+\frac{5}{192}+\frac{5}{384}\)

=>\(2\times C=\frac{10}{3}+\frac53+\frac56+\cdots+\frac{5}{96}+\frac{5}{192}\)

=>\(2\times C-C=\frac{10}{3}+\frac53+\frac56+\cdots+\frac{5}{96}+\frac{5}{192}-\frac53-\frac56-\cdots-\frac{5}{192}-\frac{5}{384}\)

=>\(C=\frac{10}{3}-\frac{5}{384}=\frac{1280}{384}-\frac{5}{384}=\frac{1275}{384}\)

\(a,\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+....+\frac{1}{384}\)

\(\text{Đ}\text{ặt}\)\(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{384}\)

\(2A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+....+\frac{1}{192}\)

\(2A-A=\frac{1}{3}-\frac{1}{384}\)

a đề sai

b)Đặt A=1/4x7 + 1/7x10 + 1/10x13 +...........+ 1/19x22

\(3A=3\left(\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{19.22}\right)\)

\(3A=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{19}-\frac{1}{22}\)

\(3A=\frac{1}{4}-\frac{1}{22}\)

\(A=\frac{9}{44}:3\)

\(A=\frac{3}{44}\)

tk

\(A=\dfrac{1}{3}\left(1+\dfrac{1}{2}+...+\dfrac{1}{256}+\dfrac{1}{512}\right)\)

Đặt B=1+1/2+...+1/256+1/512

=>2B=2+1+...+1/128+1/256

=>B=2-1/512=1023/512

=>\(A=\dfrac{1}{3}\cdot\dfrac{1023}{512}=\dfrac{341}{512}\)