Question

hãy viết thu gọn tổng sau

D= \(1+5^2+5^3+...+5^{2016}+5^{2017}\)

Answer 1

Ta có : D = 1 + 5 + 5² + ...... + 5²⁰¹⁷

=> 5D = 5 + 5² + 5³ + ...... + 5²⁰¹⁸

=> 5D - D = 5²⁰¹⁸ - 1

=> 4D = 5²⁰¹⁸ - 1

=> D = \(\frac{5^{2018}-1}{4}\)

Answer 2

5D=5+.....+5²⁰¹⁸

5D-D=5+......5²⁰¹⁸-1-5²-......-5²⁰¹⁷

4D=5^2018-1

D=5²⁰¹⁸-1/4

Answer 3

\(D=1+5+5^2+....+5^{2017}\)

\(\Rightarrow5D=5+5^2+5^3+...+5^{2018}\)

\(\Rightarrow5D-D=5^{2018}-1\)

\(\Rightarrow4D=5^{2018}-1\)

\(\Rightarrow D=\frac{5^{2018}-1}{4}\)