Question

Tính tồng S= 3+\(\frac{3}{2}\)+\(\frac{3}{2^2}\)+.............+\(\frac{3}{2^9}\)

GIải ra lời giải lun nha!!!

Answer 1

S = \(3+3.\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)\)

Đặt A = \(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)

=> 2A = \(1+\frac{1}{2}+...+\frac{1}{2^8}\)

=> 2A - A = A = \(\left(1+\frac{1}{2}+...+\frac{1}{2^8}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)=1-\frac{1}{2^9}\)

=> S = 3 + 3 . A = \(3+3.\left(1-\frac{1}{2^9}\right)=3+3-\frac{3}{2^9}=6-\frac{3}{2^9}\)