Question 140967
If you were to save 1 penny on the first day of the yesr then 2 pennies on the second day, etc, for one year, your total, S, would be:
{{{S = 1+2+3+4+...+365}}} This is called an "Arithmetic series"
The total, S, is called the partial sum and is given by:
{{{S[n] = (n/2)(a[1]+a[n])}}} where: n = the number of terms in the series (that's 365 in this problem), {{{a[1]}}} is the first term (that's 1 here) and {{{a[n]}}} is the nth term and that is {{{a[365] = 365}}}.  So...
{{{S = (365/2)(1+365)}}}
{{{S = (365/2)(366)}}}
{{{S = 65148}}} Pennies. To convert to dollars, divide by 100.
{{{S = 651.48}}} dollars.
S = $651.48