Question

Cho A = 1/2+3/2+(3/2)^2+................+(3/2)^2012; B=(3/2)^2013:2

Tính A - B

Answer 1

Lời giải:

$A-\frac{1}{2}=\frac{3}{2}+(\frac{3}{2})^2+....+(\frac{3}{2})^{2012}$

$\frac{3}{2}(A-\frac{1}{2})=(\frac{3}{2})^2+(\frac{3}{2})^3+....+(\frac{3}{2})^{2013}$

$\Rightarrow \frac{3}{2}(A-\frac{1}{2}) - (A-\frac{1}{2})=(\frac{3}{2})^{2013}-\frac{3}{2}$

$\Rightarrow \frac{1}{2}(A-\frac{1}{2})=(\frac{3}{2})^{2013}-\frac{3}{2}$

$\Rightarrow A=2(\frac{3}{2})^{2013}-\frac{5}{2}$

$\Rightarrow A-B=2(\frac{3}{2})^{2013}-\frac{5}{2}- \frac{1}{2}.(\frac{3}{2})^{2013}$

$\Rightarrow A-B=\frac{3}{2}(\frac{3}{2})^{2013}-\frac{5}{2}=(\frac{3}{2})^{2014}-\frac{5}{2}$