(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: α. 3 n Σ 4 n=1 |

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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

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Q: v that the series (-1)" is a conditionally convergent series. Then determine the least n=1 ber of…

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: Investigate whether the series ∞∑n=0ne−n converges or diverges.

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Q: 00 (n + 4)x" 2" + n n=0

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Q: Use the Root Test to determine if the series converges or diverges (-1)"2* (-1)"2ñ zuć en? (2n2 –…

A: Given problem:-

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: