Question 1091345
Your friend is saving pennies. She puts one penny into her piggy bank the first day, two pennies the second day, four the third day, and so on, doubling the number of pennies added. How many much money would she have at the end of vacation, if she could keep saving at this rate? Vacation lasts 75 days.

I would like to know if there is a formula for solving this problem, which I am fairly sure there is. I also have an understanding that the answer is very large.
<pre>Yes, there is! You need to use the formula for the sum of a GP, or a Geometric Sequence.
This is: {{{matrix(1,3, S[n], "=", a[1](r^n - 1)/(r - 1))}}}, with:
{{{S[n]}}} = Sum of "n" terms (Unknown, in this case)
{{{n}}}  = Number of terms (75, in this case)
{{{a[1]}}} = First term (1, in this case)
{{{r}}}  = Common Ratio (2, in this case)
Replacing all these variables should give you {{{highlight_green(matrix(1,8, S[n], "=", 3.77789 * 10^22, pennies, "=", "$3.77789", "*", 10^20))}}}