Tính nhanh (Tính bằng cách thuận tiện) nhé!!
Đặt A = 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
=> 2A = 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128
=> 2A - A = 1/4 - 1/256
=> A = 64/256 - 1/256
=> A = 63/256
Đặt \(A=\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+...+\frac{1}{256}\)
\(\Rightarrow A=\frac{1}{2^3}+\frac{1}{2^4}+.....+\frac{1}{2^8}\)
\(\Rightarrow2A=\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^7}\)
\(\Rightarrow2A-A=\left(\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^7}\right)-\)\(\left(\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^8}\right)\)
\(\Rightarrow A=\frac{1}{2^2}-\frac{1}{2^8}\)
\(\frac{1}{8}\)+ \(\frac{1}{16}\)+ \(\frac{1}{32}\)+\(\frac{1}{64}\)+ \(\frac{1}{128}\)+ \(\frac{1}{256}\)
= \(\frac{32}{256}\)+ \(\frac{16}{256}\)+ \(\frac{8}{256}\)+ \(\frac{4}{256}\)+ \(\frac{2}{256}\)+ \(\frac{1}{256}\)
= \(\frac{48}{256}\)+ \(\frac{8}{256}\)+ \(\frac{4}{256}\)+ \(\frac{2}{256}\)+ \(\frac{1}{256}\)
= \(\frac{56}{256}\)+ \(\frac{4}{256}\)+ \(\frac{2}{256}\)+ \(\frac{1}{256}\)
=\(\frac{60}{256}\)+ \(\frac{2}{256}\)+ \(\frac{1}{256}\)
= \(\frac{62}{256}\)+ \(\frac{1}{256}\)
= \(\frac{63}{256}\)
