Question

Rút gọn tổng : 2+2^2+2^3+....2^99+2^100

Answer 1

Gọi tổng trên là A , ta có:

A=2+2²+2³+.....+2⁹⁹+2¹⁰⁰

2A=2²+2³+2⁴+.....+2¹⁰⁰+2¹⁰¹

2A-A=(2²+2³+2⁴+....+2¹⁰⁰+2¹⁰¹)-(2+2²+2³+.....+2⁹⁹+2¹⁰⁰)

A=2¹⁰¹-2

Answer 2

Đặt A = 2 + 2² + 2³ + .... + 2⁹⁹ + 2¹⁰⁰

=> 2A =  2² + 2³ + .... + 2¹⁰⁰ + 2¹⁰¹

=> 2A - A = 2¹⁰¹ - 2

=>A =  2¹⁰¹ - 2

Answer 3

Đặt :S= 2+2^2+2^3+....2^99+2^100

=> 2S = 2^2+2^3+....2^99+2^100+2^101

=> 2S-S=S=(2^2+2^3+....2^99+2^100+2^101)-(2+2^2+2^3+....2^99+2^100)

=> S= 2^101 - 2