This assignment covers

Testing Infinite Series for Convergence

.

Questions

Test these infinite series for convergence.

State the test you use and if the series converges or diverges.

1)	2)
3)	4)
5)	6)
7)	8)
9)	10)
11)

.

Solutions

1) test for divergence	2) limit comparison test since 9/5 > 1, the series diverges.
3) basic comparison test Sb n = S (1 / 3 n ) a convergent Geometric Series r = a = 1/3 so series converges.	4) limit comparison test we apply l'Hopital's rule to the limit we get º, so the series diverges.
5) test for divergence series diverges.	6) since maximum value of cos n = 1, we know that Basic comparison test with a convergent p-series. Since
7) reminder: e is a constant < 3. so we apply l'Hopital's rule we apply the rule again twice to get But e - 3 < 0 so the fraction becomes so the series diverges. limit comparison test works too with the limit = e > 1 so diverges.	8) apply l'Hopital's rule. , l'Hopital again. , series diverges. ___________________________ 9) is a divergent p-series, p = ½ < 1 so the series diverges.
10) use the integral test we set u = ln x and du = 1/x dx so the series converges.
11) We will apply partial fraction decompostion for the Integral test. so the series converges.

.

(Back to Caculus II MathRoom Index)

.

(all content of the MathRoom Lessons © Tammy the Tutor; 2002 - 2005).