Question

[Nguyễn Quỳnh Trang]

Tính 1 + 2²  + 2⁴ + 2⁶ +......+2¹⁰⁰

Answer 1

[✰Ťøρ ²⁷ Ťɾїệʉ Vâɳ ŇD✰]

Gọi 1 + 2²  + 2⁴ + 2⁶ +......+2¹⁰⁰  là A

Có A=1 + 2²  + 2⁴ + 2⁶ +......+2¹⁰⁰ 

=>2²A=2²+2⁴+2⁶+2⁸+...+2¹⁰²

=> 4A-A=(2²+2⁴+2⁶+2⁸+...+2¹⁰²)-(1 + 2²  + 2⁴ + 2⁶ +......+2¹⁰⁰ )

3A=2¹⁰²-1

A=(2¹⁰²-1):3

Answer 2

[Gukmin]

Trả lời:

Đặt  \(A=1+2^2+2^4+2^6+...+2^{100}\)

 \(2^2A=2^2+2^4+2^6+...+2^{102}\)

 \(4A=2^2+2^4+2^6+...+2^{102}\)\(4A-A=\left(2^2+2^4+2^6+...+2^{102}\right)-\left(1+2^2+2^4+...+2^{100}\right)\)

\(3A=2^2+2^4+2^6+...+2^{102}-1-2^2-2^4-...-2^{100}\)

\(3A=\left(2^2-2^2\right)+\left(2^4-2^4\right)+...+\left(2^{100}-2^{100}\right)+\left(2^{102}-1\right)\)

\(3A=0+0+...+0+2^{102}-1\)

\(3A=2^{102}-1\)

\(A=\frac{2^{102}-1}{3}\)

Vậy\(A=\frac{2^{102}-1}{3}\)

Hok tốt!

Good girl