The following two lines indicate another way to derive the formula for the sum of the firs...

The following two lines indicate another way to derive the formula for the sum of the first n integers by rearranging the terms in the sum. Fill in the details.

How many copies of n + 1 are in there in the second line? You may need to consider the cases of odd n and even n separately. If that’s not clear, first try writing it out explicitly for n = 6 and n = 7.