Question

A= (1/5)^1+(1/5)^2+...........+(1/5)^2014+(1/5)^2015

So sánh với 1/4

Answer 1

\(A=\left(\frac{1}{5}\right)^1+\left(\frac{1}{5}\right)^{^2}+...+\left(\frac{1}{5}\right)^{2015}\)

\(A=\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{2015}}\)

\(5A=5\left(\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{2015}}\right)\)

\(5A=1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{2014}}\)

\(\Rightarrow5A-A=\left(1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{2014}}\right)-\left(\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{2015}}\right)\)

\(\Rightarrow4A=1-\frac{1}{5^{2015}}\)

\(\Rightarrow A=\frac{1-\frac{1}{5^{2015}}}{4}\)

Vì \(1-\frac{1}{5^{2015}}