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better latexing
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edit approved Mar 11 at 23:52
TShiong
edit approved Mar 11 at 23:52
TShiong
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$$\sum_{n=1}^{k}\frac{1}{n^2+n}=\frac{k}{k+1}$$

I don't think that this summation requires too much context as this is a Q&A site, but I was just wondering why the summation is evaluated so nicely. I don't have too much knowledge and creativity in evaluating sums, so is there a bunch of equations that will make this make sense instantly? If so, I haven't found it on the internet.

$\frac{k}{k+1}$ looks a lot like the formula for the geometric series. I was wondering if $$\frac{1}{r}(\frac{1}{1-r})=\frac{1}{-r^2+r}$$$$\dfrac{1}{r}\left(\frac{1}{1-r}\right)=\frac{1}{-r^2+r}$$ had anything to do with this problem.

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

I don't think that this summation requires too much context as this is a Q&A site, but I was just wondering why the summation is evaluated so nicely. I don't have too much knowledge and creativity in evaluating sums, so is there a bunch of equations that will make this make sense instantly? If so, I haven't found it on the internet.

$\frac{k}{k+1}$ looks a lot like the formula for the geometric series. I was wondering if $$\frac{1}{r}(\frac{1}{1-r})=\frac{1}{-r^2+r}$$ had anything to do with this problem.

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

I don't think that this summation requires too much context as this is a Q&A site, but I was just wondering why the summation is evaluated so nicely. I don't have too much knowledge and creativity in evaluating sums, so is there a bunch of equations that will make this make sense instantly? If so, I haven't found it on the internet.

$\frac{k}{k+1}$ looks a lot like the formula for the geometric series. I was wondering if $$\dfrac{1}{r}\left(\frac{1}{1-r}\right)=\frac{1}{-r^2+r}$$ had anything to do with this problem.

Post Closed as "Duplicate" by D S, Martin R, amWhy algebra-precalculus
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Lucien Jaccon
Lucien Jaccon
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Why is $\sum_{n=1}^{k}\frac{1}{n^2+n}=\frac{k}{k+1}$

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

I don't think that this summation requires too much context as this is a Q&A site, but I was just wondering why the summation is evaluated so nicely. I don't have too much knowledge and creativity in evaluating sums, so is there a bunch of equations that will make this make sense instantly? If so, I haven't found it on the internet.

$\frac{k}{k+1}$ looks a lot like the formula for the geometric series. I was wondering if $$\frac{1}{r}(\frac{1}{1-r})=\frac{1}{-r^2+r}$$ had anything to do with this problem.