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Here's the question:

$\sum_{i=1}^{n} \frac{1}{i^2 + i}$

How do you express this summation in terms of n?

I'm at a loss of where to go with this. I know the formulas for the summation of $i^2$ and $i$, but I'm not sure where to use these (or if it's even relevant) because the only thing I can think of is to sum the denominators and then take their reciprocal, which is clearly wrong.

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Hint: $\frac 1 {i^{2}+i}=\frac 1 i -\frac 1 {i+1}$.

[The answer is $1-\frac 1{n+1}$].

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  • $\begingroup$ ...Did not think of that at all - thanks a lot! $\endgroup$
    – Stoodent
    Jan 26, 2020 at 0:19

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