Well, I think that the issue is much more complex than you have shown here.

In fact, there is no short list of Scriptural passages that causes the reader to irresistibly conclude that the doctrine of trinity is being described.

I think it much more likely that the doctrine of trinity is a sort of religious *theory* which is alone in being in complete agreement with all Scriptures regarding the nature of the relationship between Jesus, the Father and the Holy Spirit.

Now, let me backtrack a little and explain. We can show from Scripture - despite what anyone says - that the Father and Jesus are both God (John 20:28; Heb 1:8)

We also know from Scripture that Jesus prayed to the Father, and that (while on earth, at least) he was subject to the will of the Father.

Finally, both Jesus himself and the Father in the Old Testament clearly indicate that there is only one God.

These Scriptures clearly indicate the *beginnings* of trinitarian doctrine. There is only one God; the Father and Jesus are both God; yet clearly the Father and Jesus are not the same person.

However, progressing from that point, *logically*, requires more knowledge than I possess. We know that the Holy Spirit is treated as a person in some passages in the New Testament - but does that make it a "person" of the Godhead? I can't say, but I think you will admit that mentioning the Holy Spirit in concert with the Father and Jesus is telling - especially when the phrase used is "in the name of...the Holy Spirit", indicating that the Holy Spirit is not only a person, but a person of authority at least *similar* to the Father and Jesus. This could be considered supporting evidence (not proof!) for the idea that the Holy Spirit is
a) also an integral part of the Godhead
b) is of similar *or* equal authority with the other persons mentioned


Conclusions
a) Even someone without collegiate religious education can use logic to determine that something very like the trinity is described by Scripture
b) It is difficult for that same someone to *prove* using Scripture and logic the precise details of the doctrine of trinity - that is, that all 3 persons are members of the trinity, that all 3 are "co-equal" and "co-eternal". However, such details clearly do not *contradict* Scripture, and there is evidence *supporting* (but not proving) such claims.

SO, remembering my admittedly lacking education in this area, I conclude that the doctrine of trinity is the most rational explanation of the pertinent Scriptures that is widely supported. The details may or may not be accurate or verified - *I* am not able to prove them. However, the primary premises of the doctrine can clearly be deduced from Scripture, and the more precise details are at least partially supported and never contradicted by Scripture.