Question

Tính các tổng sau

 A = 1+ 2²+ 2⁴+ 2⁶+2⁸+...+2²⁰⁰

Answer 1

tui mới học lớp 5

Answer 2

Ta có:

A = 1+2² + 2⁴+...+2¹⁰⁰

4A= 2²+2⁴+2⁶+...+2¹⁰⁰+2¹⁰²

Suy ra:

4A - A= 3A= ( 2²+2⁴+...+2¹⁰²)- (1+2²+2⁴+...+2¹⁰²)

3A= 2¹⁰²-1

A=( 2¹⁰²-1)/3

Answer 3

A=1+2^2+2^4+2^6+2^8+...+2^200

=>4A=2^2+2^4+2^6+2^8+2^10+...+2^202

=>4A-A=(2^2+2^4+2^6+2^8+...+2^202)-(1+2^2+2^4+2^6+2^8+...+2^200)

=>3A=2^202-1

=>A=(2^202-1)/3