Question

3/1*5+3/5*9+3/9*13+.....+3/81*85

Answer 1

`3/(1.5) + 3/(5.9) + ... + 3/(81.85)`

`= 3/4 . (4/(1.5) + 4/(5.9) + ... + 4/(81.85))`

`= 3/4 . (1 - 1/5 + 1/5 - 1/9+ ... + 1/81 - 1/85)`

`= 3/4 . (1 - 1/85)`

`= 3/4 . 84/85`

`=63/85`

Answer 2

\(\dfrac{3}{1.5}+\dfrac{3}{5.9}+\dfrac{3}{9.13}+...+\dfrac{3}{81.85}\)
\(=\dfrac{3}{4}.\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{81}-\dfrac{1}{85}\right)\)
\(=\dfrac{3}{4}.\left(1-\dfrac{1}{85}\right)\)
\(=\dfrac{3}{4}.\dfrac{84}{85}\)
\(=\dfrac{63}{85}\)

Answer 3