Đáp án:
$=\dfrac{5}{34}.$
Giải thích các bước giải:
Đặt tổng trên là $S.$
Ta có:
$S=\dfrac{1}{10}+\dfrac{1}{40}+\dfrac{1}{88}+\dfrac{1}{154}+\dfrac{1}{238}$
$S=\dfrac{1}{2.5}+\dfrac{1}{5.8}+\dfrac{1}{8.11}+\dfrac{1}{11.14}+\dfrac{1}{14.17}$
$S=\dfrac{1}{3}(\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}+\dfrac{3}{14.17})$
$S=\dfrac{1}{3}(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{14}-\dfrac{1}{17})$
$S=\dfrac{1}{3}(\dfrac{1}{2}-\dfrac{1}{17})$
$S=\dfrac{1}{3}.\dfrac{15}{34}$
$S=\dfrac{5}{34}.$
