Question

[nguyenvantiendung]

m = 1/3² + 2/3³ = 3/3⁴+.......+ 10/3¹¹ mn giúp mình nha

Answer 1

[Vũ Hoàng Dương]

$M=\frac{1}{3}+\frac{2}{3^2}+...+\frac{100}{3^{11}}$

$\Rightarrow 3M=1+\frac{2}{3}+\frac{3}{3^2}+...+\frac{10}{3^{10}}$

$\Rightarrow 3M-M=\left(1+\frac{2}{3}+\frac{3}{3^2}+...+\frac{10}{3^{10}}\right)-\left(\frac{1}{3}+\frac{2}{3^2}+...+\frac{10}{3^{10}}\right)$

$\Rightarrow 2M=1+\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\right)-\frac{100}{3^{100}}$

$\Rightarrow 2M=1+\frac{1}{2}-\frac{1}{3^{99}.2}-\frac{100}{3^{100}}$

$\Rightarrow M=\frac{3}{4}-\frac{1}{3^{99}.4}-\frac{50}{3^{100}}$