欢迎来到第三周的《数列与级数》 Welcome, to week 3 of Sequences and Series.
--第三周会讲些什么--
在本课程的第一周的时候 我们认识了数列 In the first week of this course, in week 1, we met sequences.
而上周 即第二周 我们了解了级数 And last week, in week 2, we met series.
现在 想想这门课程的名称 数列与级数 Now, considering that the name of this course is sequences and series.
这是否就意味着我们已经完成了这门课程？ Does that mean we're done with this course,
我们想讲的都讲到了吗？ that we've covered everything we meant to cover?
一点也不 我们才刚刚开始 Not at all, we're just getting started.
既然我们对数列与级数都有所了解了 Now that we know about sequences and series, it's time
是时候该更深层次地探讨它们了 to really dig in, and do something with these things.
尤其是 In particular,
我们将着重讨论敛散性的检验 we're going to focus on convergence tests.
给定一个级数 它是收敛的 还是发散的？ Given a series, does a converge or diverge?
对此我们早已有所了解 We've seen a little bit of this already, we've
我们学习了对级数通项式的检验 learned about the nth term test that tells us to
它告诉了我们观察该级数第n项的极限 look at the limit of the nth term of a
如果这个极限不为零 则该级数发散 series and if that limits not 0, the series diverges.
我们也学习了几何级数和比较审敛法 We've learned about geometric series, we learned about comparison
但这些都只是冰山一角 tests, but there's way more convergence tests to cover.
本周 我们将要来学习更多有趣的检验敛散性的方法 This week, we're going to be looking at these fancier convergence tests.
我们着重学习 比值审敛法 We're going to be focusing
根值审敛法 积分判别法 on the ratio test, the root
很多有趣的事情等着你哦 test and the integral test. It'll be a lot of fun.
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