Question

A=3+3^2+3^3+3^4+...+3^100

Answer 1

A=3+3^2+3^3+.....+3^100 Vậy 3A= 3^2+3^3+....+3^101 Ta lấy 3A-A = (3^2+3^3+....3^101)-(3+3^2+3^3+....+3^100) = 3^101-3.

Vậy 2A=3^101-3 hay A=(3^101-3)/2. 

Answer 2

    A=3+3^2+3^3+...+3^100

=>3A=3^2+3^3+3^4+...+3^101

=>3A-A=(3^2+3^3+3^4+...+3^101)-(3+3^2+3^3+...+3^100)

=>2A=3^101-3

=>A=\(\frac{3^{101}-3}{2}\)

Vậy A=\(\frac{3^{101}-3}{2}\)