Question

tính 1 cách hợp lí c=1/7+1/7^2+1/7^3+1/7^4+..+1/7^50+1/6.7^50

 

Answer 1

Đặt \(A=\dfrac{1}{7}+\dfrac{1}{7^2}+...+\dfrac{1}{7^{50}}\)

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

=>\(7A-A=1+\dfrac{1}{7}+...+\dfrac{1}{7^{49}}-\dfrac{1}{7}-\dfrac{1}{7^2}-...-\dfrac{1}{7^{50}}\)

=>\(6A=1-\dfrac{1}{7^{50}}\)

=>\(A=\dfrac{1}{6}-\dfrac{1}{6\cdot7^{50}}\)

\(C=A+\dfrac{1}{6\cdot7^{50}}=\dfrac{1}{6}-\dfrac{1}{6\cdot7^{50}}+\dfrac{1}{6\cdot7^{50}}=\dfrac{1}{6}\)