Question

cho A= 1+2 mũ 1+ 2 mũ 2+ 2 mũ 3+......+ 2 mũ 2007

a) Tính 2A

b) Chứng minh: A= 2 mũ 2008 -1

Answer 1

Lời giải:
a.

A=1+21+22+23+....+22007A=1+21+22+23+....+22007

2A=1.2+21.2+22.2+23.2+....+22007.22A=1.2+21.2+22.2+23.2+....+22007.2

2A=2+22+23+24+....+220082A=2+22+23+24+....+22008

b.

A=2A−A=(2+22+23+24+...+22008)−(1+2+22+...+22007)A=2A−A=(2+22+23+24+...+22008)−(1+2+22+...+22007)

=22008−1=22008−1 (đpcm)

Answer 2

a) Ta có :

A = 1 + 2¹ + 2² + ... + 2²⁰⁰⁷

=> 2A = 2 . ( 1 + 2¹ + 2² + ... + 2²⁰⁰⁷ )

=> 2A = 2¹ + 2² + 2³ + ... + 2²⁰⁰⁸

b) Ta có : 2A = 2¹ + 2² + 2³ + ... + 2²⁰⁰⁸ ( phần a )

Mà A = 1 + 2¹ + 2² + ... + 2²⁰⁰⁷

=> 2A - A = ( 2¹ + 2² + 2³ + ... + 2²⁰⁰⁸ ) - ( 1 + 2¹ + 2² + ... + 2²⁰⁰⁷ )

=> A = 2²⁰⁰⁸ - 1

Answer 3

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