6. (1 point) Prove that if (an+ba) diverges. bn diverges, then an converges and nel KSB: 0MFA CIN 8. (1 point) Find the total length of the zigzag path. Note that each bounce meets a side at a right angle and bounces off at a 30° angle. 30% L 6. (1 point) Prove that if (an+ba) diverges. bn diverges, then an converges and nel KSB: 0MFA CIN 8. (1 point) Find the total length of the zigzag path. Note that...
Please prove why this series diverges! 3 n2 - 2 (sum does not converge) n=1 4n25 +n
The sum diverges. Use the limit test to prove it. Determine if the series is convergent or divergent. If the series is absolutely convergent, note that in the summary. For the summary: 1. Clearly indicate which test you are using. 2. Verify that the series meets the requirements for that test. 3. Clearly summarize the results of the test. (n!)" 2 nan n=1
1. Consider the sequence a,-_(1 + (-1)") for all n є N. rove that a (b) Prove that (an) diverges using subsequences
diverges. (You can use anything we've shown in class through today's video Prove that lecture, 4/9) n
2. Prove that the infinite series Ex=1(-1)k diverges. (Hint: Compute the first few terms of the sequence of partial sums and determine a formula for the nth partial sum, Sn. Using this, give a formal proof, starting with the definition for divergence of this series. (Additional reference: Workshop Week #7)
2. Let (%)-1 be a bounded sequence and let (h) .1 be a sequence that diverges to oo. Prove that (an +bn)ni diverges to oo
part e and f 0 for all k E N and Σ at oo. For each of the following, either prove that the given series con- 4. Suppose ak verges, or provide an example for which the series diverges. ak 1 + at ar ai ak 0 for all k E N and Σ at oo. For each of the following, either prove that the given series con- 4. Suppose ak verges, or provide an example for which the series...
Let .Which one of the following tables is completed correctly? Σ001 un Diverges Converges Diverges Diverges Diverges Converges Converges Converges Diverges Diverges Σ001 un Diverges Converges Diverges Diverges Diverges Σ001 Un Converges Converges Converge Converges Converges Converges Converges Converges Converges Converges Converges Converge Converges Converges Converges Converges Converges Converges Converges Converges Converge Converges Converges Diverges Diverges Question 1 1 pts Which one of the following is the Taylor polynomial of degree 3 for the function f(x) - sin 3z about...
(1) Suppose that Σ an converges and Σ bn diverges. Show that Σ (an +b.) diverges. (1) Suppose that Σ an converges and Σ bn diverges. Show that Σ (an +b.) diverges.