Question

Tính \(B=-\frac{4}{5}+\frac{4}{5^2}-\frac{4}{5^3}+...+\frac{4}{5^{200}}\)

Answer 1

\(-5B=4-\frac{4}{5}+\frac{4}{5^2}-....-\frac{4}{5^{199}}\)

\(-5B-B=4-\frac{4}{5^{200}}\)

\(-6B=\frac{4\left(5^{200}-1\right)}{5^{200}}\)

\(B=\frac{2\left(1-5^{200}\right)}{5^{200}.3}\)

Answer 2

Ta có:\(B=...\)

\(\Leftrightarrow5B=-4+\frac{4}{5}-\frac{4}{5^2}+...+\frac{4}{5^{199}}\)

\(\Leftrightarrow5B+B=-4+\frac{4}{5^{200}}\)

\(\Leftrightarrow6B=-4+\frac{4}{5^{200}}\Rightarrow B=\frac{-4+\frac{4}{5^{200}}}{6}=\frac{-2+\frac{2}{5^{200}}}{3}\)