Question

Chứng minh: 1/7 mũ 2 - 1/7 mũ 4 +1/7 mũ 6-1/7 mũ8 +......+1/7 mũ 98-1/7 mũ 100<1/50

Answer 1

Đặt \(A=\dfrac{1}{7^2}-\dfrac{1}{7^4}+\dfrac{1}{7^6}-\dfrac{1}{7^8}+...+\dfrac{1}{7^{98}}-\dfrac{1}{7^{100}}\)

\(7^2.A=1-\dfrac{1}{7^2}+\dfrac{1}{7^4}-\dfrac{1}{7^6}+...+\dfrac{1}{7^{96}}-\dfrac{1}{7^{98}}\)

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

\(A+49.A=1-\dfrac{1}{7^{100}}\)

\(50A=1-\dfrac{1}{7^{100}}< 1\)

\(A< \dfrac{1}{50}\)