Question

Tính tổng B = 1 + 5 + \(5^2+5^3+...+5^{2008}+5^{2009}\)

Answer 1

\(B=1+5+5^2+5^3+...+5^{2008}+5^{2009}\)
Đặt \(5B=5.\text{ (}1+5+5^2+5^3+...+5^{2008}+5^{2009}\text{)}\)
\(\Rightarrow5B=5+5^2+5^3+...+5^{2009}+5^{2010}\)
\(\Rightarrow5B-B=\left(5+5^2+5^3+...+5^{2009}+5^{2010}\right)-\left(1+5+5^2+...+5^{2009}\right)\)\(\Rightarrow4B=5^{2010}-1\)
\(\Rightarrow B=\dfrac{5^{2010}-1}{4}\)
Vậy \(B=\dfrac{5^{2010}-1}{4}\)