What is the sum of the following geometric series:
1+1/4+1/16
looks like a GS where
a = 1 , r = 1/4
but with only 3 terms, why not just add them up
1 + 1/4 + 1/16
= (16 + 4 + 1)/16
= 21/16
To find the sum of a geometric series, we need to determine two things: the first term of the series (a) and the common ratio (r).
In this case, the series starts with the term 1, which is our first term (a). The common ratio (r) can be found by dividing any term in the sequence by its previous term.
Let's calculate the common ratio (r) for this series:
r = (1/4) / 1 = 1/4
Now that we know the first term (a = 1) and the common ratio (r = 1/4), we can use the formula for the sum of a geometric series:
Sum = a / (1 - r)
Let's substitute the values we found into the formula:
Sum = 1 / (1 - 1/4)
Now, let's simplify the expression:
Sum = 1 / (3/4)
Sum = 4/3
Therefore, the sum of the geometric series 1 + 1/4 + 1/16 is 4/3.