Since my brother died recently but did not have a Will, if I send a copy of his death certificate to the bills he has remaining, is that enough?

Did your brother have assets when he passed away?  If he had assets that passed into his estate, his creditors can file a claim in the estate.  If he had no assets, or all the assets passed to others outside the estate, then there is nothing for the creditors to take.  In that case, you can send them the death certificate.  If you contact your brother's creditors, you can expect them to call and contact you about his assets and paying the bills.  If you don't want to bother with this, don't contact them at all.  You have no obligation to contact them.