In this lesson, we will learn how to determine whether a series is convergent or divergent by comparing it to a series of known convergence using the comparison test.
Students will be able to
Q1:
Use the comparison test to decide whether the series ∞237𝑛+1.1 is convergent or divergent.
Q2:
Let 𝑎=𝑛+1𝑛−𝑛+4𝑛+28. As 𝑛→∞, we see that 𝑎≈1𝑛, which suggests that ∞𝑎 is a divergent series. Verify this by finding the first integer 𝑛 where 𝑎>1𝑛. You should check that this inequality remains true for all larger 𝑛.
Q3:
Consider the series ∞𝑛𝑛=11+24+39+⋯sinsinsinsin.
Do the terms 𝑎 of this sequence tend to 0 as 𝑛→∞?
Is the series convergent or divergent?
Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.