Đáp án: $S = \dfrac{1100}{91}$
Giải thích các bước giải:
Ta có : $S= \bigg(1+\dfrac{6}{6}\bigg).\bigg(1+\dfrac{6}{14}\bigg).\bigg(1+\dfrac{6}{24}\bigg)....\bigg(1+\dfrac{6}{126}\bigg)$
$ = \dfrac{6+6}{6}.\dfrac{14+6}{14}.\dfrac{24+6}{24}....\dfrac{126+6}{126}$
$ = \dfrac{12}{6}.\dfrac{20}{14}.\dfrac{30}{24}....\dfrac{132}{126}$
$ = \dfrac{3.4}{1.6}.\dfrac{4.5}{2.7}.\dfrac{5.6}{3.8}....\dfrac{11.12}{9.14}$
$ = \dfrac{3.4.4.5.5.6....11.12}{1.6.2.7.3.8....9.14}$
$ = \dfrac{(3.4.5....11).(4.5.6....12)}{(1.2.3....9).(6.7.8....14)}$
$ = \dfrac{10.11.4.5}{13.14}$
$ = \dfrac{5.11.4.5}{13.7}$
$ = \dfrac{1100}{91}$
Vậy $S = \dfrac{1100}{91}$
