Question

Tính nhanh: A = 2 phần 3 + 1 phần 3 + 1 phần 15 + 1 phần 75 + 1 phần 375 +1 phần 1875

(phần là dấu gạch phân số nha!)

 

Answer 1

\(A=\frac{2}{3}+\frac{1}{3}+\frac{1}{15}+\frac{1}{75}+\frac{1}{375}+\frac{1}{1875}\)

\(A=\left(\frac{2}{3}+\frac{1}{3}\right)+\frac{1}{15}+\frac{1}{75}+\frac{1}{375}+\frac{1}{1875}\)

\(A=1+\left(\frac{5}{75}+\frac{1}{75}\right)+\frac{1}{375}+\frac{1}{1875}\)

\(A=1+\frac{6}{75}+\frac{1}{375}+\frac{1}{1875}\)

\(A=1+\left(\frac{150}{1875}+\frac{1}{1875}\right)+\frac{1}{375}\)

\(A=1+\frac{151}{1875}+\frac{1}{375}\)

\(A=1+\left(\frac{151}{1875}+\frac{5}{1875}\right)\)

\(A=1+\frac{156}{1875}\)

\(A=\frac{1875}{1875}+\frac{156}{1875}\)

\(A=\frac{677}{625}\)

Answer 2

\(A=\frac{2}{3}+\frac{1}{3}+\frac{1}{15}+\frac{1}{75}+\frac{1}{375}+\frac{1}{1875}\)

\(\Leftrightarrow A=\left(\frac{2}{3}+\frac{1}{3}\right)+\left(\frac{1}{15}+\frac{1}{75}\right)+\left(\frac{1}{375}+\frac{1}{1875}\right)\)

\(\Leftrightarrow A=1+\left(\frac{5}{75}+\frac{1}{75}\right)+\left(\frac{5}{1875}+\frac{1}{1875}\right)\)

\(\Leftrightarrow A=1+\frac{6}{75}+\frac{6}{1875}\)

\(\Leftrightarrow A=1+\frac{2}{25}+\frac{2}{625}\)

\(\Leftrightarrow A=1+\left(\frac{2}{25}+\frac{2}{625}\right)\)

\(\Leftrightarrow A=1+\left(\frac{50}{625}+\frac{2}{625}\right)\)

\(\Leftrightarrow A=1+\frac{52}{625}\)

\(\Leftrightarrow A=\frac{677}{625}\)

Answer 3

=\(\frac{677}{625}\)