# Math

This is hard to explain...
I need to spend between \$20,000 and \$60,000, BUT I need to spend ALL amounts, like \$1, then 2, then 3, then 4
How do I figure out how much I will spend when I'm finished?

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1. Let n=last amount you spend, then when you add up 1, 2, 3, 4, ....n-1, n, you get the total as n(n+1)/2.
Solve for n as between the solutions of the following equations:
n(n+1)/2 = 60000 ...(1)
n(n+1)/2 = 20000 ...(2)

Solution to (1) is 345.9, and
solution to (2) is 199.5.

So any integer between 200 and 345 can be the 'last amount'. And the corresponding total amount can be calculated.

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