# Math Help - [SOLVED] Sequence involving largest integer function.

1. ## [SOLVED] Sequence involving largest integer function.

Let $(a_n)$be the sequence defined by $a_n = [\frac{n^2 + 8n +10}{n+9}]$ where (x) is the largest integer that does not exceed x, Find the value of $\sum_{n=1}^{30}a_n$ ??

2. Hello wizard654zzz
Originally Posted by wizard654zzz
Let $(a_n)$be the sequence defined $a_n = [\frac{n^2 + 8n +10}{n+9}]$ where (x) is the largest integer that does not exceed x, Find the value of $\sum_{n=1}^{30}a_n$ ??
Divide and get quotient and remainder:
$\frac{n^2 + 8n +10}{n+9}=(n-1) + \frac{19}{n+9}$
Now for $1\le n\le 10, \;2>\frac{19}{n+9}\ge 1$. Hence $a_n = n$.

But for $n > 10, \;\frac{19}{n+9}<1$. Hence $a_n = n-1$.

$1+2+3+...+10+10+11+12+...+29 = 445$