# Deriving formula of series and then finding value at a limit

So the question follows:

You post an update to social media that begins to garner attention. Within the first minute, you gain 1 new follower, in the second minute you gain another 2, in the third you gain another 4, in the fourth another 8, and so on.

(a) Assuming that the pattern continues, use the formula for a geometric sum to find a simple expression for your total number of new followers Fk at the end of к minutes.

(b) The population of the world is approximately 7.4 billion. How many minutes will it take before the whole planet is following your success in calculus?

So essentially, I interpreted this as a series with these values: 1, 3, 7, 15...

So my

a (first term) = 1

r (multiplier)= an - an-1

Where n and n-1 are subscripts.

How would I put this into the geometric series formula (a)/(1-r)

• You're using the wrong formula. – studrayght5 Oct 30 '15 at 3:30

$F_k=\sum_{i=0}^{k-1}2^{i}=\frac{1-2^{k}}{1-2}=2^k-1$ and evaluate the inequality. $F_k \geq 7400000000$ if $2^k-1 \geq 7.4 \times 10^9$ if $2^k \geq 7.4\times10^9-1$ if $k \geq \frac{ln(7.4\times10^9-1)}{ln(2)}$
Realize that the $nth$ term is just $2^n-1$.