Question

Tính nhanh

A=1/2 + 1/4 + 1/8 + .... + 1/256

B= 5/1.2 + 5/3.4 +....+ 5/91.92

Answer 1

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

\(2A=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{128}\)

\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{128}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\right)\)

\(A=1-\frac{1}{256}=\frac{255}{256}\)

\(B=\frac{5}{1.2}+\frac{5}{3.4}+...+\frac{5}{91.92}\)

\(B=5.\left(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{91.92}\right)\)

\(B=5.\left(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{91}-\frac{1}{92}\right)\)

\(B=5.\left(\frac{1}{47}+\frac{1}{48}+...+\frac{1}{92}\right)\)

Answer 2

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

\(A=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{8}\right)+...+\left(\frac{1}{128}-\frac{1}{256}\right)\)

\(A=1-\frac{1}{256}=\frac{255}{256}\)

Answer 3

Ta có : \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+.....+\frac{1}{256}\)

\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+.....+\frac{1}{128}\)

\(2A-A=1-\frac{1}{256}\)

\(A=\frac{255}{256}\)

Answer 4

\(B=\frac{5}{1.2}+\frac{5}{3.4}+...+\frac{5}{91.92}\)

\(B=5.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{91}-\frac{1}{92}\right)-\frac{5}{2.3}\)

\(B=5.\left(1-\frac{1}{92}\right)-\frac{5}{2.3}=5.\frac{91}{92}-\frac{5}{2.3}=\frac{455}{92}-\frac{5}{2.3}=\frac{1135}{276}\)