1. Definition
Split the term so intermediate terms cancel: 1/(k(k+1))=1/k−1/(k+1), giving sum n/(n+1).
3. Properties & Laws
- 1/(k(k+1))=1/k−1/(k+1);
- Sum = 1−1/(n+1)=n/(n+1);
- Tends to 1 as n→∞;
- Similar odd-denominator forms.
4. Steps
- Enter n;
- Click "Sum";
- Or click "Load Example".
5. Worked Examples
Example: n=10 gives 10/11≈0.9091.
6. Common Pitfalls
Balance coefficients after splitting;
Identify the surviving ends;
It approaches, not equals, 1.