Question

D = 4/5 + 4/5 ^ 2 - 4/5 ^ 3 + ...... + 4/5 ^ 200

mong trả lời sớm

Answer 1

oki

Answer 2

\(D=-\dfrac{4}{5}+\dfrac{4}{5^2}-\dfrac{4}{5^3}+...+\dfrac{4}{5^{200}}\)

\(\Rightarrow D=4\left(-\dfrac{1}{5}+\dfrac{1}{5^2}-\dfrac{1}{5^3}+...+\dfrac{1}{5^{200}}\right)\)

\(5D=4\cdot\left(-1+\dfrac{1}{5}-\dfrac{1}{5^2}+...+\dfrac{1}{5^{199}}\right)\)

\(\Rightarrow5D+D=4\cdot\left(-1+\dfrac{1}{5}-\dfrac{1}{5^2}+...+\dfrac{1}{5^{199}}-\dfrac{1}{5}+\dfrac{1}{5^2}-\dfrac{1}{5^3}+...+\dfrac{1}{5^{200}}\right)\)

\(\Rightarrow6D=4\cdot\left(\dfrac{1}{5^{200}}-1\right)\)

\(\Rightarrow D=\dfrac{2}{3}\cdot\left(\dfrac{1}{5^{200}}-1\right)\)

Answer 3

Answer 4

\(D=\dfrac{4}{5}+\dfrac{4}{5}^2+\dfrac{4}{5}^3+...+\dfrac{4}{5}^{200}\)

\(\dfrac{4}{5}D=\dfrac{4}{5}^2+\dfrac{4}{5}^3+...+\dfrac{4}{5}^{201}\)

\(\dfrac{4}{5}D-D=\dfrac{4}{5}^{201}-\dfrac{4}{5}\)

\(-\dfrac{1}{5}D=\dfrac{4}{5}^{201}-\dfrac{4}{5}\)

\(D=\dfrac{\dfrac{4}{5}-\dfrac{4}{5}^{201}}{\dfrac{1}{5}}=4-\dfrac{4^{201}}{5^{200}}\)