∑ (n=1) to ∞ (n+7) / (n^2+14n+6) ∫(upward)∞ (downward)c dn = ?

Question

∑ (n=1) to ∞ (n+7) / (n^2+14n+6) ∫(upward)∞ (downward)c dn = ? (Evaluate your integral with bottom limit c=1.)

Answer 1

Alex:

I have no clue what integral you need to evaluate.

For the series ∑(n+7)/(n²+14n+6)

Notice when n is large, (n+7)/(n²+14n+6) = n/n² = 1/n

So determining the convergence or divergence of ∑(n+7)/(n²+14n+6) is the same as determining the convergence or divergence of ∑(1/n). Does ∑(1/n) converge or diverge?