Question

tính gọn: A=\(1+2^2+2^3+2^4+...+2^{1000}\)

 

Answer 1

A=2¹⁰⁰⁰+...+2⁴+2³+2²+1

=2¹⁰⁰¹-2¹⁰⁰⁰+...+2⁵-2⁴+2⁴-2³+2³-2²+1

=2¹⁰⁰¹-4+1=2¹⁰⁰¹-3

Answer 2

 

A= 1 + 2² + 2³ + ... + 2¹⁰⁰⁰

2A= 2 + 2² + 2³ + ... + 2¹⁰⁰¹

2A-A= (2 + 2² + 2³ + ... + 2¹⁰⁰¹)-(1 + 2² + 2³ + ... + 2¹⁰⁰⁰)

=>A=2¹⁰⁰¹-1.