At one point in time the Lord accepted dead sacrifices. The periodic shedding of the blood of animals sufficed. However since Jesus Christ shed His blood on the Cross, God requires us to gives our lives to Him in a different manner. As born again believers we are to be living sacrifices. Now we must learn to die to our old sinful selves. Every part of us should be a sacrifice to the Lord.
‘Reasonable service’ can be understood as saying, ‘this is what you should do.’ When someone does something nice for you that usually makes you more inclined to help them when they ask. God the Son gave His very life just for you! And now He has called us to give our lives back to Him. He gave His all to you. The least you can do is give your all back to Him. This is what you should do!