Question

B= 7 + 7^{3 +} 7⁵ + 7⁷ +...+ 7⁹⁹

Answer 1

\(B=7+7^3+7^5+...+7^{99}\\ 49B=7^3+7^5+7^7+...+7^{101}\\ 49B-B=\left(7^3+7^5+7^7+...+7^{101}\right)-\left(7+7^3+7^5+...+7^{99}\right)\\ 48B=7^{101}-7\\ B=\dfrac{7^{101}-7}{48}\)

Vậy \(B=\dfrac{7^{101}-7}{48}\)

Answer 2

\(B=7+7^3+7^5+...+7^{99}\)

\(\Rightarrow7^2.B=7^3+7^5+7^7+...+7^{99}+7^{101}\)

Hay \(49B=7^3+7^5+7^7+...+7^{99}+7^{101}\)

\(\Rightarrow48B=49B-B=7^{101}-7\)

\(\Rightarrow B=\dfrac{7^{101}-7}{48}\)

Vậy \(B=\dfrac{7^{101}-7}{48}\)

tik mik nha !!!