These words all mean to have an idea that sth is true or possible or to have a particular opinion about sb/sth.以上各词均含以为、认为之义。
think to have an idea that sth is true or possible, although you are not completely certain; to have a particular opinion about sb/sth指认为、以为某人/某事…但不肯定：◆Do you think (that) they'll come?你认为他们会来吗？◆Well, I like it. What do you think?嗯，我喜欢这个。你认为怎么样？
believe to have an idea that sth is true or possible, although you are not completely certain; to have a particular opinion about sb/sth指认为、以为：◆Police believe (that) the man may be armed.警方认为那个人可能携有武器。
think or believe?用 think 还是 believe？
When you are expressing an idea that you have or that sb has of what is true or possible, believe is more formal than think. It is used especially for talking about ideas that other people have; think is used more often for talking about your own ideas.表达自己或别人认为真实或有可能的想法时，believe 较 think 正式。believe 尤用于别人的想法；think 较常用于自己的想法：◆Police believe…警方认为…◆I think…我认为… When you are expressing an opinion, believe is stronger than think and is used especially for matters of principle; think is used more for practical matters or matters of personal taste.表达意见时，believe 语气较 think 强烈，尤用于原则性事情；think 多用于实际事情或个人喜好。
feel to have a particular opinion about sth that has happened or about what you/sb ought to do指认为（已发生的事情…）、相信（应该…）：◆We all felt (that) we were unlucky to lose.我们都认为我们输了是运气不好。
reckon(informal) to think that sth is true or possible指认为、以为：◆I reckon (that) I'm going to get that job.我认为我会得到那份工作。
be under the impression that… to have an idea that sth is true指以为某事…：◆I was under the impression that the work had already been completed.我还以为已经完工了呢。
Patterns
to think/believe/feel/reckon/be under the impression that…
It is thought/believed/reckoned that…
to be thought/believed/felt/reckoned to be sth
to think/believe/feel sth about sb/sth
to sincerely/honestly/seriously/mistakenly think/believe/feel
