Question

Cho A= 1+2+2²+...+2²⁰⁰  . Hãy viết A+1 dưới dạng lũy thừa.

 

Answer 1

2A = 2+2^2 + 2^3 + ...+2^200 + 2^201

2A - A =( 2+2^2 + 2^3 + ...+2^200 + 2^201)-(1+2+2^2 + 2^3 + ...+2^200 )

=> A = 2^201 - 1

=> A+1 = 2^201

Answer 2

A = 1+2=2²+...+2²⁰⁰

2A=2+2²+2³+...+2²⁰¹

2A-A=(2+2²+2³+...+2²⁰¹)-(1+2=2²+...+2²⁰⁰)

A=2²⁰¹-1

=>A+1=2²⁰¹-1+1=2²⁰¹

Vậy A =2²⁰¹