Verified answer

Setting the Σ for the limit, you should get...

lim n→∞ Σ(a_n / b_n)

Well, this can be expressed in integral, which gives us...

∫^(-∞,∞) a_n/b_n

If we have the converging series, then ∫^(-∞,∞) a_n/b_n = L, noting that it's the Riemann Sum!

Good luck!