Question

Rút gọn:

2+2²+2³+...+2¹⁰⁰

 

Answer 1

Đặt 

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

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

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

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

Answer 2

Đặt A = 2 + 2² + 2³ + ... + 2¹⁰⁰

2A = 2² + 2³ + 2⁴ + ... + 2¹⁰¹

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

A = 2¹⁰¹ - 2

Answer 3

Gọi A=2+2^2+2^3+....+2^100

Suy ra 2A= 2(2+2^2+2^3+...+2^100)

                 = 2^2+2^3+2^4+...+2^101

Do đó 2A-A=(2^2+2^3+2^4+...+2^100+2^101)-(2+2^2+2^3+2^4+...+2^100)

Hay A=2^2+2^3+2^4+...+2^100+2^101-2-2^2-2^3-...-2^100

=2^101-2

Vậy biểu thức đã cho sau khi rút gọn là 2^101-2

Answer 4

=(2+2²+2³+2⁴)+(2⁵+2⁶+2⁷+2⁸)+...+(2⁹⁷+2⁹⁸+2⁹⁹+2¹⁰⁰)

=2.(1+2+2²+2³⁾+2⁵.(1+2+2²+2³⁾+...+2⁹⁷.(1+2+2²+2³)

=2.15+2⁵.15+2⁹⁷.15

Tu lm tiep nha

Answer 5

Đặt A = 2 + 2² + 2³ + ... + 2¹⁰⁰

2A = 2² + 2³ + 2⁴ + ... + 2¹⁰¹

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

A = 2¹⁰¹ - 2