Question

Evaluate the series 50 + 10 + 2 + . . .

Answer 1

It is a sum of geometric series, where first term
`a_1=50` and common ratio:


`r=(a_2)/(a_1)=(10)/(50)=(1)/(5)`

so:


`S=50+10+2+\ldots=(a_1)/(1-r)=(50)/(1-(1)/(5))=(50)/((4)/(5))=(50\cdot5)/(4)=(250)/(4)=\boxed{62.5}`