Question

Tính tổng: 2+2^2+2^3+...+2^2015

Answer 1

đặt A= 1+2+2^2+2^3+...+2^99+2^100

=>2A=2+2²+2³+...+2¹⁰⁰+2¹⁰¹

=>2A-A=2+2²+2³+...+2¹⁰⁰+2¹⁰¹-(1+2+2²+2³+...+2⁹⁹+2¹⁰⁰)

=> A=2+2²+2³+...+2¹⁰⁰+2¹⁰¹-1-2-2²-2³-...-2⁹⁹-2¹⁰⁰

=2¹⁰¹-1

vậy 1+2+2^2+2^3+...+2^99+2^100=2¹⁰¹-1

Answer 2

Đặt A = 2 + 2² + 2³ + ... + 2²⁰¹⁵

=> 2A = 2² + 2³ + 2⁴ + ... + 2²⁰¹⁶

=> 2A - A = ( 2² + 2³ + 2⁴ + ... + 2²⁰¹⁶ ) - ( 2 + 2² + 2³ + ... + 2²⁰¹⁵ )

=> A = 2²⁰¹⁶ - 2

Vậy A = 2²⁰¹⁶ - 2

Answer 3

Đặt tổng đó là A = 2 + 2² + 2³ + ... + 2²⁰¹⁵

2A = 2² + 2³ + 2⁴ + ... + 2²⁰¹⁶

2A - A = 2² + 2³ + 2⁴ +... + 2²⁰¹⁶ - 2 + 2² + 2³ + ... + 2²¹⁰⁵

=> A = 2²⁰¹⁶ - 2

Answer 4

\(A=2+2^2+2^3+...+2^{2015}.\)

\(2A=2\left(2+2^2+2^3+...+2^{2015}\right)\)

\(2A=2^2+2^3+2^4+...+2^{2016}\)

\(2A-A=2^{2016}-2\)

\(=>A=2^{2016}-2\)