Question

Cho A=2/3+8/9+26/27+...+3^n -1/3^n. Chứng minh A>n-1/2

Answer 1

cho A= 2/3+8/9+26/17+...+3^n-1/3^n n-A= 1/3+1/3^2+1/3^3+...+1/3^n 3(n-A)= 3+1/3+1/3^2+..+1/3^n-1 3(n-A)-(n-A)=1-1/3^n 2(n-A)=1-1/3^n n-A=1/2-2/3^n<1/2 =>n-A<1/2 => A

Answer 2

cho A=\(\frac{2}{3}+\frac{8}{9}+\frac{26}{27}+...+\frac{3^n-1}{3^n}\)

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

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

=> \(3\left(n-A\right)-\left(n-A\right)=2\left(n-A\right)=1-\frac{1}{3^n}\)

=>\(2\left(n-A\right)< 1\)

=>\(n-A< \frac{1}{2}\)

=> \(A< n-\frac{1}{2}\)

Deu la tui het do

Answer 3

Sao lại là n-A thế bạn? n đã tìm đc đâu

Answer 4

n-A là cái j zậy