(a) State the conditions that must be satisfied in order to apply the integral test to deter- ine the convergence or divergence of a given series. (b) Use the integral test to determine whether the following series is convergent or diver- ent. You can assume that the conditions you stated in part (a) are satisfied (you don't need to emonstrate these, just go ahead and use the test).

Q: The interval of convergence of the series (4x-12)" is Zn=0 -3)-+" (n+1) Select one: True O False

A: We can find the interval of convergence by using the ratio test .

Q: ∞ Σ(-1)^²-¹ (2 −1) en n=1

A:

Q: 1 n * (In n) n=2 8.

A:

Q: Find the largest interval (in x) where the series summation from n = 1 to infinite of xe-nx…

A: Here we use D'Almbert ratio test.

Q: We want to use the Alternating Series Test to determine if the series: k² k6+ 18 Σ(-1)*+2 k=4…

A:

Q: 71.Š-1)"(nº + 1) en (-1)"(п3 + 1) 2. п4 + 1 (-1)"(п3 + 1) 3. 00 –1)" п3 +7

A: According to our guidelines, I solve first 3 subparts. Kindly request you to post the remaining…

Q: Find the values of p for which the series En-1- liverges. (-1) en² converges and

A: Given that, the series is      , then          .

Q: 5. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

A:

Q: 3. Determine and justify whether the series In(i) i=1 converges or diverges.

A: for the given, we would like to test whether the series converges or diverges.

Q: 5. Use the Integral test to determine whether the series k converges or diverges Ak*+1 You do not…

A:

Q: 4. Consider the following tests: n-th Term , Integral, Direct Comparison, Limit Comparison, Ratio,…

A: