Câu hỏi của Nguyễn thị meo

Question

B=1+2+3 mũ 2+3mũ 3 +...+3 mũ 50 +3 mũ 51

nguyễn tuấn thảo · Accepted Answer

$B=1+2+3^2+\cdot\cdot\cdot+3^{51}$

$\Rightarrow B=3+3^2+3^3+\cdot\cdot\cdot+3^{51}$

$\Rightarrow3B=3^2+3^3+\cdot\cdot\cdot+3^{52}$

$\Rightarrow3B-B=\left(3^2+\cdot\cdot\cdot+3^{52}\right)-\left(3+\cdot\cdot\cdot+3^{51}\right)$

$\Rightarrow2B=3^{52}-3$

$\Rightarrow B=\frac{3^{52}-3}{2}$

Câu trả lời:

$B=1+2+3^2+\cdot\cdot\cdot+3^{51}$

$\Rightarrow B=3+3^2+3^3+\cdot\cdot\cdot+3^{51}$

$\Rightarrow3B=3^2+3^3+\cdot\cdot\cdot+3^{52}$

$\Rightarrow3B-B=\left(3^2+\cdot\cdot\cdot+3^{52}\right)-\left(3+\cdot\cdot\cdot+3^{51}\right)$

$\Rightarrow2B=3^{52}-3$

$\Rightarrow B=\frac{3^{52}-3}{2}$

๖²⁴ʱČʉէε✦ɠїɾℓ༉ · Answer

$1+2+3^2+3^3+...+3^{50}+3^{51}$

Đặt tổng trên là A ta có :

$A=3+3^2+3^3+...+3^{50}+3^{51}$

$3A=3^2+3^3+3^4+...+3^{51}+3^{52}$

$3A-A=\left(3^2+...+3^{52}\right)-\left(3+...+3^{51}\right)$

$2A=3^{52}-3$

$A=\frac{3^{52}-3}{2}$

Vậy...

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