Question

Find to infinity the sum of sequence 1 , 9/10 , (9/10)^2,(9/10)^3​

Answer 1

`S=(a)/(1-r)` if
`|r| < 1`.

`r=(9)/(10)`

`\left|(9)/(10)\right|=(9)/(10) < 1` therefore, the sum exists.

`S=(1)/(1-(9)/(10))=(1)/((1)/(10))=10`