- #1
Skynt
- 39
- 1
Can anyone explain this property of shifting the index on the summation notation?
I'm reading a book and came across this which has confused me. I don't see how these are equal:
[tex]\sum_{k=1}^n \frac{1}{k(k+1)} = \frac{1}{2} + \sum_{k=2}^{n+1} \frac{1}{k(k-1)}[/tex]
It's part of an explanation that proves that the zeta function converges for values equal to or larger than 2. I just fail to see how they're equal.
I'm reading a book and came across this which has confused me. I don't see how these are equal:
[tex]\sum_{k=1}^n \frac{1}{k(k+1)} = \frac{1}{2} + \sum_{k=2}^{n+1} \frac{1}{k(k-1)}[/tex]
It's part of an explanation that proves that the zeta function converges for values equal to or larger than 2. I just fail to see how they're equal.
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