TÍNH 3H30 ĐI HỌC ỒI Ạ
\(A=11\times\left(\dfrac{5}{11\times16}+\dfrac{5}{16\times21}+\dfrac{5}{21\times26}+\dfrac{5}{26\times31}+\dfrac{5}{31\times36}+\dfrac{5}{36\times41}\right)\)
\(=11\times\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{31}+\dfrac{1}{31}-\dfrac{1}{36}+\dfrac{1}{36}-\dfrac{1}{41}\right)\)
\(=11\times\left(\dfrac{1}{11}-\dfrac{1}{41}\right)\)
\(=1-\dfrac{11}{41}=\dfrac{30}{41}\)
Ta có:
\(A=\dfrac{55}{11\times16}+\dfrac{55}{16\times21}+...+\dfrac{55}{36\times41}\)
\(=11\times\left(\dfrac{5}{11\times16}+\dfrac{5}{16\times21}+...+\dfrac{5}{36\times41}\right)\)
\(=11\times\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{36}-\dfrac{1}{41}\right)\)
\(=11\times\left(\dfrac{1}{11}-\dfrac{1}{41}\right)\)
\(=11\times\dfrac{30}{451}\)
\(=\dfrac{30}{41}\)
