Question

So sánh: A= 1+7+\(7^2+7^3+...+7^{100}\)với B=\(7^{101}\).

Answer 1

\(A=1+7+7^2+7^3+...+7^{100}\)

\(\Rightarrow7A=7+7^2+7^3+7^4+...+7^{101}\)

\(\Rightarrow7A-A=7^{101}-1\)

\(\Rightarrow6A=7^{101}-1< 7^{101}\)

Vậy : \(A< B\)

Answer 2

\(A=1+7+7^2+7^3+...+7^{100}\)

\(7A=7+7^2+7^3+7^4+....+7^{101}\)

\(7A-A=\left(7+7^2+7^3+...+7^{101}\right)-\left(1+7+7^2+....+7^{100}\right)\) \(6A=7^{101}-1\)

\(A=\dfrac{7^{101}-1}{6}< 7^{101}\)

\(\Rightarrow A< B\)

Vậy....................................................

Answer 3