Question

tính nhanh

cho A=1/3-1/3^2+1/3^3-1/3^4+...+1/3^99-1/3^100

Answer 1

Ta có: 

\(A=\frac{1}{3}-\frac{1}{3^2}+\frac{1}{3^3}-\frac{1}{3^4}+...+\frac{1}{3^{99}}-\frac{1}{3^{100}}\)

=> \(3A=1-\frac{1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+...+\frac{1}{3^{98}}-\frac{1}{3^{99}}\)

=> \(A+3A=1-\frac{1}{3^{100}}\)

=> \(4A=\frac{3^{100}-1}{3^{100}}\)

=> \(A=\frac{3^{100}-1}{4.3^{100}}\)