Question

tính tổng 1+5+5^2+5^3+5^4+...5^2016

Answer 1

Đặt T=1+5+5^2+5^3+5^4+...5^2016

5T=5(1+5+5^2+5^3+5^4+...5^2016)

5T=5+5²+5³+...+5²⁰¹⁷

5T-T=(5+5²+5³+...+5²⁰¹⁷)-(1+5+5^2+5^3+5^4+...5^2016)

4T=5²⁰¹⁷-1

T=(5²⁰¹⁷-1)/4

Answer 2

Gọi S =\(1+5+5^2+5^3+5^4+...+5^{2016}\)

\(\Rightarrow5S=5.\left(1+5+5^2+5^3+5^4+...+5^{2016}\right)\)

\(\Rightarrow5S=5+5^2+5^3+5^4+...+5^{2016}\)\(+5^{2017}\)

\(\Rightarrow5S-S=5+5^2+5^3+5^4+...+5^{2016}\)\(+5^{2017}\)\(-\left(1+5+5^2+5^3+5^4+...+5^{2016}\right)\)

\(\Rightarrow4S=5^{2017}-1\)