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In a normal problem solving I run into a sum:

$\sum_{k=1}^n \frac{10}{10+k}$

Let $n=20$ or something like that (not huge). Browsing a list of sums and another, I'm not finding a formula for this one.

I'm wondering is it possible to find a formula for this type of sum, or if this type of sum has to be computed by a computer summing it.

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    http://math.stackexchange.com/questions/5035/1-1-2-1-3-1-n2011-01-15

1 Answers 1

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You can express it using the Harmonic numbers as $\sum_{k=1}^n \frac{10}{10+k}=10(H_{10+n}-H_{10})\approx 10(\ln(10+n)-\ln(10))$ But if you want it exactly you need to add it up.

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    @Americo: You are right. I didn't read carefully. Fixed2011-01-15