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1275.

Why the formula works:

The formula for the first n integers comes from the following idea.

Make a list of all n integers, let us just say 5 to make it easy to see.

1,2,3,4,5

Now write them again , but start with 5.

5,4,3,2,1

Now write them one on top of the other

1,2,3,4,5

5,4,3,2,1

If you add those two lists, column by column, each column has a total of 6.

5+1, 4+2, 3+3 etc.

And since it was the numbers 1-5, there are 5 columns.

So we have 5x6 as a total so far. But we counted each number twice sine we wrote them twice. So now to fix that we need to divided by2 and we have 5x6 divided by2=15

The general formula for the first n integers starting with 1 is

n(n+1)/2

So in this case it is (50)(51)/2=51x25=1275

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Q: What is the sum total of integers 1 to 50?
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