Question

8/1*5+8/5*9+8/9*13+.....+8/41*45

Answer 1

`8/(1.5) + 8/(5.9) + ... + 8/(41 . 45) `

`= 2 . (4/(1.5) +4/(5.9) + ... + 4/(41 . 45) )`

`= 2 . (1 - 1/5 + 1/5 - 1/9 + ... + 1/41 - 1/45)`

`= 2 . (1 - 1/45) `

`= 2 . 44/45`

`= 88/45`

Answer 2

\(\dfrac{8}{1\cdot5}+\dfrac{8}{5\cdot9}+\dfrac{8}{9\cdot13}+...+\dfrac{8}{41\cdot45}\)

\(=2.\left(\dfrac{1}{1\cdot5}+\dfrac{1}{5\cdot9}+\dfrac{1}{9\cdot13}+...+\dfrac{1}{41\cdot45}\right)\)

\(=2.\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{41}-\dfrac{1}{45}\right)\)

\(=2.\left(1-\dfrac{1}{45}\right)\)

\(=2\cdot\dfrac{44}{45}\)

\(=\dfrac{88}{45}\)

Answer 3