Question

Hãy tính 

\(A=1+2+^{2^2}+^{2^3}+...................+^{2^{100}}\)

Answer 1

 A = 1+2+2²+2³+...........+2¹⁰⁰

=>2A = 2+2²+2³+2⁴+..............+2¹⁰¹

=> 2A - A = 2¹⁰¹-1

=> A = 2¹⁰¹ - 1

Answer 2

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

=>2A-A=(2+2^2+2^3+2^4+...+2^101)-(1+2+2^2+2^3+...+2^100)

=>2A-A=2^101-1

hay A=2^101-1

Answer 3

=>2A=2+2²+2³+2⁴+.........+2¹⁰¹

=>2A-A=(2+2²+2³+2⁴+....+2¹⁰¹)-(1+2+2²+2³+........+2¹⁰⁰)

=>A=2¹⁰¹-1+2¹⁰⁰