Question

[Nguyễn thị meo]

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

Answer 1

[nguyễn tuấn thảo]

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

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

\(\Rightarrow3B=3^2+3^3+\cdot\cdot\cdot+3^{52}\)

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

\(\Rightarrow2B=3^{52}-3\)

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

Answer 2

[๖²⁴ʱČʉէε✦ɠїɾℓ༉]

\(1+2+3^2+3^3+...+3^{50}+3^{51}\) 

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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