Question

Tính :

\(B=\dfrac{45}{12\cdot21}+\dfrac{45}{21\cdot31}-\dfrac{40}{24\cdot34}-\dfrac{40}{34\cdot44}-\dfrac{40}{44\cdot54}-\dfrac{40}{54\cdot64}\)

Answer 1

ta có B = \(\dfrac{45}{12.21}+\dfrac{45}{21.30}-\left(\dfrac{40}{24.34}+...+\dfrac{40}{54.64}\right)\)

\(=5\left(\dfrac{9}{12.21}+\dfrac{9}{21.30}\right)-4\left(\dfrac{10}{24.34}+...+\dfrac{10}{54.64}\right)\)

\(=5\left(\dfrac{1}{12}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{30}\right)-4\left(\dfrac{1}{24}-\dfrac{1}{34}+\dfrac{1}{34}-\dfrac{1}{44}+...+\dfrac{1}{54}-\dfrac{1}{64}\right)\)

\(=5\left(\dfrac{1}{12}-\dfrac{1}{30}\right)-4\left(\dfrac{1}{24}-\dfrac{1}{64}\right)\)

\(=5.\dfrac{1}{20}-4.\dfrac{5}{192}\)

\(=5.\dfrac{1}{20}-\dfrac{4}{192}.5\)

\(=5\left(\dfrac{1}{20}-\dfrac{4}{192}\right)=5.\dfrac{7}{240}=\dfrac{7}{48}\)