S=5^2/1×6+5^2/6×11+5^2/11×16+5^2/16×21+5^2/21×26 12/10/2021 Bởi Serenity S=5^2/1×6+5^2/6×11+5^2/11×16+5^2/16×21+5^2/21×26
Đáp án: $S=\dfrac{125}{26}$ Giải thích các bước giải: Ta có: $S=\dfrac{5^2}{1\cdot 6}+\dfrac{5^2}{6\cdot 11}+\dfrac{5^2}{11\cdot 16}+\dfrac{5^2}{16\cdot 21}+\dfrac{5^2}{21\cdot 26}$ $\to S=\dfrac{5\cdot 5}{1\cdot 6}+\dfrac{5\cdot 5}{6\cdot 11}+\dfrac{5\cdot 5}{11\cdot 16}+\dfrac{5\cdot 5}{16\cdot 21}+\dfrac{5\cdot 5}{21\cdot 26}$ $\to S=\dfrac{5\cdot (6-1)}{1\cdot 6}+\dfrac{5\cdot (11-6)}{6\cdot 11}+\dfrac{5\cdot (16-11)}{11\cdot 16}+\dfrac{5\cdot (21-16)}{16\cdot 21}+\dfrac{5\cdot (26-21)}{21\cdot 26}$ $\to S=5\cdot(\dfrac11-\dfrac16)+5\cdot(\dfrac16-\dfrac1{11})+5\cdot(\dfrac1{11}-\dfrac1{16})+5\cdot (\dfrac1{16}-\dfrac1{21})+5\cdot(\dfrac1{21}-\dfrac1{26})$ $\to S=5\cdot(\dfrac11-\dfrac16+\dfrac16-\dfrac1{11}+\dfrac1{11}-\dfrac1{16}+\dfrac1{16}-\dfrac1{21}+\dfrac1{21}-\dfrac1{26})$ $\to S=5\cdot (1-\dfrac1{26})$ $\to S=\dfrac{125}{26}$ Bình luận
Đáp án: $S=\dfrac{125}{26}$
Giải thích các bước giải:
Ta có:
$S=\dfrac{5^2}{1\cdot 6}+\dfrac{5^2}{6\cdot 11}+\dfrac{5^2}{11\cdot 16}+\dfrac{5^2}{16\cdot 21}+\dfrac{5^2}{21\cdot 26}$
$\to S=\dfrac{5\cdot 5}{1\cdot 6}+\dfrac{5\cdot 5}{6\cdot 11}+\dfrac{5\cdot 5}{11\cdot 16}+\dfrac{5\cdot 5}{16\cdot 21}+\dfrac{5\cdot 5}{21\cdot 26}$
$\to S=\dfrac{5\cdot (6-1)}{1\cdot 6}+\dfrac{5\cdot (11-6)}{6\cdot 11}+\dfrac{5\cdot (16-11)}{11\cdot 16}+\dfrac{5\cdot (21-16)}{16\cdot 21}+\dfrac{5\cdot (26-21)}{21\cdot 26}$
$\to S=5\cdot(\dfrac11-\dfrac16)+5\cdot(\dfrac16-\dfrac1{11})+5\cdot(\dfrac1{11}-\dfrac1{16})+5\cdot (\dfrac1{16}-\dfrac1{21})+5\cdot(\dfrac1{21}-\dfrac1{26})$
$\to S=5\cdot(\dfrac11-\dfrac16+\dfrac16-\dfrac1{11}+\dfrac1{11}-\dfrac1{16}+\dfrac1{16}-\dfrac1{21}+\dfrac1{21}-\dfrac1{26})$
$\to S=5\cdot (1-\dfrac1{26})$
$\to S=\dfrac{125}{26}$