Hello Andrey! I disagree with Alexey. A prayer service is also a divine service, only in a short form. "Effect", as you put it, of course, is. Ordinary, believing people, as well as clergymen, will earnestly, with all their hearts, pray for the people whom you, for example, have entered. And believe me, collective prayer is much stronger than one person's prayer. However, the same as collective work.
No, there is no sense in prayer services. There are no laws of nature that would prove that a religious ritual or any words of a priest can somehow influence global problems (cure cancer, defeat hunger or an epidemic, strengthen the ruble or something like that). We have been using the only way to somehow influence this world since the very appearance of man - we work, invent, create new technologies and machines that cure diseases, build houses, melt steel and make our life better or worse.