Question

If you save one dollar on January 1, two dollars on January 2, three dollars on January 3, and continue this patter for one year, what will be the value of your entire saving, in dollars, at the end of that one year? Express your answer as a decimal.

Answer 1

This is just the sum of the first 365 integers, assuming the year is not a leap year.
There is a formula for the sum of the first n integers:\[n(n+1)/2\]
If you need to show how this is derived have a look at http://mathcentral.uregina.ca/QQ/database/QQ.02.06/jo1.html

You can see that the answer is reasonable since it should be roughly the 'average' dollar value per day multiplied by the number of days.