Question

Tính S = 1 / 5 x 9 + 1 / 9 x 13 + 1 / 13 x 17 + ....... + 1 / 41 x 45

Giải thích giúp tôi nếu trong phép tính có 1 / 4 

             

Answer 1

\(S=\dfrac{1}{5\cdot9}+\dfrac{1}{9\cdot13}+\dfrac{1}{13\cdot17}+....+\dfrac{1}{41\cdot45}\)

\(S=\dfrac{1}{4}\cdot\left(\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+\dfrac{4}{13\cdot17}+....+\dfrac{4}{41\cdot45}\right)\)

\(S=\dfrac{1}{4}\cdot\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{17}+....+\dfrac{1}{41}-\dfrac{1}{45}\right)\)

\(S=\dfrac{1}{4}\cdot\left(\dfrac{1}{5}-\dfrac{1}{45}\right)\)

\(S=\dfrac{1}{4}\cdot\dfrac{8}{45}=\dfrac{2}{45}\)