our file_123.pdf * + X File | C:/Users/bonbo/Downloads/file_123.pdf G K ... Thuong Truy Cap G Google - Hoat don.. M Gmail YouTube | Canvas Discovery P.. Razer 3 of 3 - + [ Page view | A Read aloud | Add text | Draw Highlight Erase | 6 8 9 | 7 5. (2 points) Determine whether this series converges or diverges by p-series test. 00 1 n=1 Series or Test Conclusions Comments Divergence Test This test cannot prove For any series _, a,, evaluate lim an- If lim an = 0, the test is in-conclusive If lim an * 0, the series diverges. convergence of a series. Geometric Series If -1 1 or r 1 . the series converges . For p = 1, we have the If p S 1, the series diverges . harmonic series Ell_1= Comparison Test If an S b. for all n 2 N and El-1 b,, converges, then ypically used for a series For En- d,, with non-negative terms, compare with a Eme d. converges. similar to a geometric series, known series En-, ba. If an 2 b. for all n 2 N and 21-, b,, diverges, then En-, a, harmonic, or p-series. Limit Comparison Test and 2n=1 by Typically used for a series For En-1 , with positive terms, compare with a series both converge or both diverge. similar to a geometric or p- Zn-1 b,, by evaluating L = lim um If L = 0 and En-1 by converges, then 2n- an converges series. If L = oo and Emo b, diverges, then Yme, a, diverges. Integral Test If there exists a positive, continuous, decreasing IN f(x) dx and En-, a,, both converge or both diverge. Limited to those series for which the corresponding function f such that function f can be easily an = f(n) for all n 2 N , evaluate J f(x) dx. integrated. Alternating Series If buti S b, for all n 2 1 and b,, -+ 0, then the series Only applies to alternating For En-, (-1)"ti b,, or _,(-1)" b, converges. series. Ratio Test If 0 5 p 1 or p = co, the series diverges, factorials or exponentials. Lim If p = 1, the test is inconclusive. Root Test If 0 S p 1 or p = co, the series diverges. p = lim VIal. If p = 1, the test is inconclusive. 16 C Cloudy T O 6:58 PM 5/5/2022