Bạn tham khảo :
$A = \dfrac{1}{2} + \dfrac{1}{2.2} + \dfrac{1}{2.2.2} + ... + \dfrac{1}{2 .2.2.2.2.2.2.2.2.2}$
$A = \dfrac{1}{2} +\dfrac{1}{2^2}+\dfrac{1}{2^3} + ...+\dfrac{1}{2^{10}}$
$\dfrac{1}{2}A = \dfrac{1}{2^2}+\dfrac{1}{2^3} +\dfrac{1}{2^4} ...+\dfrac{1}{2^{11}}$
$\dfrac{1}{2}A - A =( \dfrac{1}{2^2}+\dfrac{1}{2^3} +\dfrac{1}{2^4} ...+\dfrac{1}{2^{11}}) - ( \dfrac{1}{2} +\dfrac{1}{2^2}+\dfrac{1}{2^3} + ...+\dfrac{1}{2^{10}})$
$ \dfrac{-1}{2}A = \dfrac{1}{2^{11}} - \dfrac{1}{2}$
$A = \dfrac{1}{2^{11}} - \dfrac{1}{2} + \dfrac{-1}{2}$
$A = \dfrac{1}{2^{11}} - (-1)$
$A = \dfrac{1}{2^{11}} +1$
