Question

Tính giá trị của A : 

A=1+2+2^2+2^3+...+2^98+2^99+2^100

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

ta có :

   A = 1 + 2 + 2 ^ 2 + 2 ^ 3 + ... + 2 ^98 + 2 ^ 99 + 2 ^ 100

   A = 2⁰ + 2¹ + 2² + 2³ + ... + 2⁹⁹ + 2¹⁰⁰

 2A = 2¹ + 2² + 2³ + 2⁴ + ... + 2¹⁰⁰ + 2¹⁰¹

2A - A = ( 2¹ + 2² + 2³ + 2⁴ + ... + 2¹⁰⁰ + 2¹⁰¹ ) - ( 2⁰ + 2¹ + 2² + 2³ + .. + 2¹⁰⁰ )

  A  = 2¹⁰¹ - 2⁰

       = 2¹⁰¹ - 1 .