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arithmetic series sum (1 Viewer)
- Thread starter enigma_1
- Start date
RealiseNothing
what is that?It is Cowpea
This is actually a special sum known as a "telescoping sum". It means that all terms in the sum will cancel out except for the first and last. If you write out the sum like they have said to you will get:
+ (\frac{1}{2}-\frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + ... + (\frac{1}{n} - \frac{1}{n-1}))
You can see now that this is indeed a telescoping sum by writing it as such:
 + (\frac{1}{3} - \frac{1}{3}) + (\frac{1}{4} - \frac{1}{4}) + ... + (\frac{1}{n-1} - \frac{1}{n-1}) + \frac{1}{n})
So the sum is just:
You can see now that this is indeed a telescoping sum by writing it as such:
So the sum is just: