Moscow Middle School Math Olympiad Question | Find the general formula for this special sum

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What is the general formula for this special sum? This is a question from Moscow Mathematical Olympiad. In this video, we'll apply a powerful identity to find out the general formula for this special sum.

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In case that one does not know this identity (like me), we may solve for the coef's through partical fraction decomposition A/k +B/(k+1)+C/(k+2), leading to A=1/2, B=-1 and C=1/2. From there, whether or not further splitting the middle term 1/(k+1), the sum is then straightforward.

ranshen