1 n+00 2 n=1 A sequence {$n} of partial sums of the series an has the property that lim Sn = Which of the following is true? 1 (a) lim an = 0. (b) lim an (c) lim an does not exist. (d) There is no way to determine the value of lim an. n+00 noo n+00 n+00 1 n The sequence {en} of partial sums of the series an has the property that sn = n=1 for every positive...
2. Prove that lim (-1)"+1 = 0. n-00 n
Question 9 00 Find Š (min 4 (n+1) Submit Question Question 10 00 n-1 Given the series $(-9 n=1 Does this series converge or diverge? O diverges O converges If the series converges, find the sum: Submit Question
2n2-31+1 b. lim cos 1. Find the following limits: a. lim 1 00 --- 3n2+4 n-00
Theory 00 2. Prove that if Vlan] < 1 then an converges. n=1
Determine whether the series is convergent or divergent. 00 + en 4 n(n + 1) n = 1 convergent divergent If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.) 8.6558 X
Find the interval of convergence for the given power series. (2 - 4)" 00 n=1 nl - 3)" The series is convergent from 2 = , left end included (enter Yor N): right end included (enter Y or N): to C = CI" 10.2 Suppose that (14 + 2) n=0 Find the first few coefficients. Со = C1 C2 C3 C4 Find the radius of convergence R of the power series. R= 2 The function f(x) is represented as a...
3. Find: 7T (1) lim n sin (3) lim arcsin G n-00 n 100 COS- n n00 n 1 (4) lim (1+ (6) lim (n+1 n) n- 3n n-00 1/n (2) lim arctann Vn2 - 1 (5) lim 2n In (1+) (8) lim n (11) lim n+ n 2+1 (14) lim n- 75n+2 (9) lim (nt n-00 700 n->00 n (7) lim V (Vn+1- Vn) (-1)"n (10) lim n+ on+1 (13) lim (3" +5")1/n sinn (12) lim arctan 2n 2n...
1) Show that Σ COSNTT N converges/diverges. N-1 2) Find the sum Σ e-N N-1 00 n 3) Show that Σ converges/diverges n=1 + 1
2. By using ratio test, R = ...? 1.0.C =....? 00 -1)n-1xn n3 n=1