TITLE: Can't simplify this summation
QUESTION [0 upvotes]: 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.

REPLY [2 votes]: Hint: $\frac 1 {i^{2}+i}=\frac  1 i -\frac  1 {i+1}$. 
[The answer is $1-\frac  1{n+1}$].
{"set_name": "stack_exchange", "score": 0, "question_id": 3522640}