Question

tính hợp lí

a)\(\frac{45x16-17}{45x15-28}\)

b)\(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)

c)136.68+16x272

Answer 1

Đặt \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)

\(\Leftrightarrow\)\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\)

\(\Leftrightarrow\)\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\right)\)

\(\Leftrightarrow\)\(2A=1-\frac{1}{3^8}\)

\(\Leftrightarrow\)\(2A=\frac{3^8-1}{3^8}\)

\(\Leftrightarrow\)\(A=\frac{3^8-1}{3^8}:2\)

\(\Leftrightarrow\)\(A=\frac{3^8-1}{3^8}.\frac{1}{2}\)

\(\Leftrightarrow\)\(A=\frac{3^8-1}{2.3^8}\)

Answer 2

b)   Đặt  \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+.....+\frac{1}{3^8}\)

\(\Rightarrow\)\(3A=1+\frac{1}{3}+\frac{1}{3^2}+....+\frac{1}{3^7}\)

\(\Rightarrow\)\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+....+\frac{1}{3^8}\right)\)

\(\Rightarrow\)\(2A=1-\frac{1}{3^8}\)

\(\Rightarrow\)\(A=\frac{1-\frac{1}{3^8}}{2}\)