Câu hỏi của Lê Thảo Nguyên

Question

Tính C = 2 + 2 mũ 2 + 2 mũ 3 +...+ 2 mũ 100

Lê Tài Bảo Châu · Accepted Answer

$C=2+2^2+2^3+...+2^{100}$

$2C=2^2+2^3+2^4+...+2^{101}$

$2C-C=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2+2^2+...+2^{100}\right)$

$C=2^{101}-2$

Câu trả lời:

$C=2+2^2+2^3+...+2^{100}$

$2C=2^2+2^3+2^4+...+2^{101}$

$2C-C=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2+2^2+...+2^{100}\right)$

$C=2^{101}-2$

Kiệt Nguyễn · Answer

$C=2+2^2+2^3+...+2^{100}$

$\Rightarrow C=2^2+2^3+2^4...+2^{101}$

$\Rightarrow2C-C=2^2+2^3+2^4...+2^{101}-2-2^2-2^3-...-2^{100}$

$\Rightarrow C=2^{101}-2$

$\Rightarrow C=2\left(2^{100}-1\right)$

Câu trả lời:

$C=2+2^2+2^3+...+2^{100}$

$\Rightarrow C=2^2+2^3+2^4...+2^{101}$

$\Rightarrow2C-C=2^2+2^3+2^4...+2^{101}-2-2^2-2^3-...-2^{100}$

$\Rightarrow C=2^{101}-2$

$\Rightarrow C=2\left(2^{100}-1\right)$