Question

1+2+2²+2³+...+2⁹⁹+2^100.

 

Answer 1

Đặt A = 1+2+2²+2³+...+2⁹⁹+2¹⁰⁰

2A = 2 ( 1+2+2²+2³+...+2⁹⁹+2¹⁰⁰ )

=2+2²+2³+...+2¹⁰⁰+2¹⁰¹

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

A = 2¹⁰¹-1

Answer 2

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

=> 2A = 2 + 2² + ......... + 2¹⁰¹ ( 2 )

Từ 2 vế của ( 1 ) và ( 2 ) Cho nhau được A = 2¹⁰¹ - 1

Answer 3

Đặt A=\(1+2+2^2+2^3+...+2^{99}+2^{100}\)

     2A=\(2\cdot\left(1+2+2^2+2^3+...+2^{99}+2^{100}\right)\)

     2A=\(2+2^2+2^3+2^4+...+2^{100}+2^{101}\)

  2A-A=\(\left(2+2^2+2^3+2^4+...+2^{100}+2^{101}\right)-\left(1+2+2^2+2^3+...+2^{99}+2^{100}\right)\)

       A=\(2^{101}-1\)

Answer 4

Đặt A= \(1+2+2^2+2^3+...+2^{99}+2^{100}\)

2A=\(2\left(1+2^2+2^3+....+2^{99}+2^{100}\right)\)

=\(2+2^2+2^3+.....+2^{101}\)

2A-A= \(2+2^2+2^3+....+2^{100}+2^{101}\)\(-\left(1+2+2^2+2^3+....+2^{99}+2^{100}\right)\)

A=\(2^{101}-1\)