Question

tính tổng

A=1/3+1/3^2+1/3^3+....+1/3^100

 

Answer 1

3A=1+1/3+1/3^2+...........+1/3^99

3A-A=1-1/3^100

A=(1-1/3^100):2

Answer 2

A = 1/3 + 1/3^2 + 1/3^3 + ... + 1/3^100

A : 3 = 1/3. ( 1/3 + 1/3^2 + ... + 1/3^100 )

A : 3 = 1/3^2 + 1/3^3 + ... + 1/3^101

A - A : 3 = 1/3 + 1/3^2 + ... + 1/3^100 - 1/3^2 - 1/3^3 - ... - 1/3^101

A . 2/3 = (1/3^2 - 1/3^2) + (1/3^3 - 1/3^3) + ... + (1/3^100 - 1/3^100) + ( 1/3 - 1/3^101 )

A . 2/3 = 0 + 0 + 0 + ... + 0 + 1/3 - 1/3^101

A . 2/3 = 1/3 - 1/3^101

=> A = 1/2 - 1/3^100.2