Let $f(a)$ be the sequence defined by $$f(a)=\left[\frac{a^2+8a+10}{a+9}\right]$$ where $[x]$ is the largest integer that does not exceed $x$.
Find the value of $$\sum_{x=1}^{30}f(x).$$
Summation of a sequence
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sequences-and-series
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2A rather straightforward method would be to compute it with the aid of, say, a computer. – 2012-06-19