Rút gọn C = 1/3 + 1/3^4 + 1/3^7 + 1/3^10 + 1/3^13

Đáp án:

$C=\dfrac{9-\dfrac1{3^{13}}}{26}$.

Giải thích các bước giải:

$C=\dfrac13+\dfrac1{3^4}+\dfrac1{3^7}+\dfrac1{3^{10}}+\dfrac1{3^{13}}\\\Rightarrow 3^3C=3^3.\!\left(\dfrac13+\dfrac1{3^4}+\dfrac1{3^7}+\dfrac1{3^{10}}+\dfrac1{3^{13}}\right)\\\Rightarrow 27C=3^2+\dfrac13+\dfrac1{3^4}+\dfrac1{3^7}+\dfrac1{3^{10}}\\\Rightarrow 27C-C=\left(3^2+\dfrac13+\dfrac1{3^4}+\dfrac1{3^7}+\dfrac1{3^{10}}\right)-\left(\dfrac13+\dfrac1{3^4}+\dfrac1{3^7}+\dfrac1{3^{10}}+\dfrac1{3^{13}}\right)\\\Rightarrow 26C=3^2-\dfrac1{3^{13}}\\\Rightarrow C=\dfrac{9-\dfrac1{3^{13}}}{26}$