Find the sum of the following geometric progression: `1,\ -1//2,\ 1//4,\ -1//8dot`

Explanation

We know that, sum of GP for infinity `= a/(1 – r) Given: `a = 1, r = (-1/2)/1 = -1/2`

Now let us substitute the values in `a/(1 – r)`

`= 1/(1 – (-1/2))`

`= 1/(1 + 1/2)`

`= 1/((2 + 1)/2)`

` = 1/(3/2) = 2/3`