Question

[Nguyễn Thị Trang]

Bài 1: Tính tổng sau:

a) 5/2 + 5/6 + 5/18 + 5/54 + 5/162

b) 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256

     giải giúp mk và kb nha!!!!!!!!!!!!!

Answer 1

[Trần Minh Quang]

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

Answer 2

[Xyz OLM]

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