Đáp án: $S=\dfrac{125}{26}$
Giải thích các bước giải:
Ta có:
$S=\dfrac{5^2}{1\cdot 6}+\dfrac{5^2}{6\cdot 11}+\dfrac{5^2}{11\cdot 16}+\dfrac{5^2}{16\cdot 21}+\dfrac{5^2}{21\cdot 26}$
$\to S=\dfrac{5\cdot 5}{1\cdot 6}+\dfrac{5\cdot 5}{6\cdot 11}+\dfrac{5\cdot 5}{11\cdot 16}+\dfrac{5\cdot 5}{16\cdot 21}+\dfrac{5\cdot 5}{21\cdot 26}$
$\to S=\dfrac{5\cdot (6-1)}{1\cdot 6}+\dfrac{5\cdot (11-6)}{6\cdot 11}+\dfrac{5\cdot (16-11)}{11\cdot 16}+\dfrac{5\cdot (21-16)}{16\cdot 21}+\dfrac{5\cdot (26-21)}{21\cdot 26}$
$\to S=5\cdot(\dfrac11-\dfrac16)+5\cdot(\dfrac16-\dfrac1{11})+5\cdot(\dfrac1{11}-\dfrac1{16})+5\cdot (\dfrac1{16}-\dfrac1{21})+5\cdot(\dfrac1{21}-\dfrac1{26})$
$\to S=5\cdot(\dfrac11-\dfrac16+\dfrac16-\dfrac1{11}+\dfrac1{11}-\dfrac1{16}+\dfrac1{16}-\dfrac1{21}+\dfrac1{21}-\dfrac1{26})$
$\to S=5\cdot (1-\dfrac1{26})$
$\to S=\dfrac{125}{26}$
