Question

Put one (1) dollar in a jar every week for fifty two (52) weeks, every week, increase the amount of money you put into the par by one (1) dollar, so the 2nd week you'll put in two dollars, fifth week five dollars etc...

How do I figure out the answer using an equation without adding 1+2+3..+51+52 and so on?

Answer 1

The final week (52) = n
(n(n+1))/2

Answer 2

\[
1+2+...+n-1+n = \sum_{k=1}^n k = \frac{n(n+1)}{2}
\]In this case they are asking for :\[
1+2+...+24+25 = \sum_{k=1}^{25} k = \frac{(25)((25)+1)}{2}
\]

Answer 3

Whoops.. they're asking for: \[
1+2+...+51+52 = \sum_{k=1}^{52} k = \frac{(52)((52)+1)}{2}
\]