For each of the following, fill in the blanks to complete the description of the test. Then, put together a complete argument for why the accompanying series converges or diverges. If the series converges, state what value it converges to. Geometric Series: A geometric series with e 0 converges to if and diverges if 2+3 5T n-2 Telescoping Series: To find the sum of a convergent telescoping series, 1. Find 2. Then _and diverges if The series converges if (n-1) Divergence Test: diverges if A series We know nothing if () Integral Test: Cos State the assumptions: and diverges if The series an Converges if_ Σ 2n 5

(c) Find the sum of each of the following series. Ent (ii) 00 8 n=2 n = 2 40 X

Determine whether the series Σ e5n n=0 converges or diverges. If it converges, find its sum. Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The series diverges because it is a geometric series with |r| 21. The series diverges because OB. lim e5n #0 or fails to exist. - n→∞ The series converges because k OC. lime5n fails to exist. k→∞ n=0 The series converges because lim e5n = 0. The sum of the OD. n→∞o series is (Type an exact answer.) The series converges because it is a geometric series with |r| < 1. O E. The sum of the series is (Type an exact answer.)

For each of the following series, write ”geometric” or ”not geometric” as appropriate, and explain why. Then, if the series is geometric and convergent, find the sum of the series. Show your work, and circle your final answer.