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Hi,

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.

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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