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I'm working through some questions in Apostol's Calculus text (vol. 1). The problem is with ex. 7 on p.64. Here, he states that

"by changing the index of summation, note that

[tex]\sum_{n=a}^{b-1} [\frac{na}{b}] = \sum_{n=a}^{b-1} [\frac{a(b-n)}{b}][\tex] "

I'm comfortable with the solution from this point on. I just don't see how these two are equivalent.

Any help would be appreciated!

p.s. Sorry about the LaTeX not displaying properly.

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# Apostol & floor function problem

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