\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}\)

= \(\left(\frac{1}{3}+\frac{1}{6}\right)+\left(\frac{1}{12}+\frac{1}{24}\right)+\left(\frac{1}{48}+\frac{1}{96}\right)+\frac{1}{192}\)

=               \(\left(\frac{1}{2}+\frac{1}{8}\right)+\left(\frac{1}{32}+\frac{1}{192}\right)\)

=                              \(\frac{5}{8}+\frac{1}{192}\)

=                                    \(\frac{121}{192}\)

ko ai bết đâu

=\(\dfrac{64}{192}+\dfrac{32}{192}+\dfrac{16}{192}+\dfrac{8}{192}+\dfrac{4}{192}+\dfrac{2}{192}+\dfrac{1}{192}\)

= \(\dfrac{127}{192}\)

= \(\frac{3071}{3072}\)nha !

chắc vậy ! 

ko đúng

N=7/2(2/1.3+....+2/13.15)

N=7/2.(1/1-1/3+.....+1/13-1/15)

N=7/2.(1-1/15)

N=7/2.(14/15)

N=7.14/2.15

Bạn giải M luôn dc ko?

\(=2\left(\frac{1}{3}+\frac{1}{6}+...+\frac{1}{192}\right)\)

\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+...+\frac{1}{96}-\frac{1}{192}\right)\)

\(=2\left(1-\frac{1}{192}\right)\)

\(=2\times\frac{191}{192}\)

\(=\frac{191}{96}\)

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

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

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

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

\(A=\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+...+\dfrac{1}{192}\)

\(2A=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{96}\)

\(A=\dfrac{1}{3}-\dfrac{1}{192}=\dfrac{64}{192}-\dfrac{1}{192}=\dfrac{63}{192}=\dfrac{21}{64}\)