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In this lesson, we will learn how to identify whether a series is divergent or convergent using the comparison test.
Q1:
Use the comparison test to decide whether the series β π = 1 π ο 2 3 7 π + 1 . 1 is convergent or divergent.
Q2:
Let π = π + 1 π β π + 4 π + 2 8 π 2 3 2 . As π β β , we see that π β 1 π π , which suggests that β π = 1 π ο π is a divergent series. Verify this by finding the first integer π where π > 1 π π . You should check that this inequality remains true for all larger π .
Q3:
Consider the series β π = 1 2 ο π π = 1 1 + 2 4 + 3 9 + β― s i n s i n s i n s i n .
Do the terms π π of this sequence tend to 0 as π β β ?
Is the series convergent or divergent?
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