2. Test the Series for convergence or divergence. In(n) Σ(-) Σ- 4 n=3 η=1 n 3. Determine which option is absolutely converges and explain in details the reason. 1 (=Σ(-1)" 3 =Σ(-1)" C-Σ(-1)* tan(n) η Υ -Σ-1): E = None of these n!
prove Σ() (")- ("). η +η - η m-k k=0
Which is series divergent? ο Σ=1 1,000,000+η 1 1 Σ=1 1.2 1 Σ En=l n2 Σ=1 an+1
2-15 Determine whether the series is convergent or divergent. 1 2. Σ 1.0001 3. Σ 1-0.00 n=5 η n=1 σο 2 3 4. Σ 5. Σ (1) ده است + ηψη 3 n=1 1 1 6. Σ 7. Σ η=5 (η – 4)? 2n + 3 n=1
η? -1 Find the sum of the series Σ on=1 (η2 +1)?
What is the limit definition of the integral cos x dx? lim Σ COS (1): η. lim Σ COS η. (1) (1) lim Σ COS T in Σων (1)
(a) Starting with the geometric series X?, find the sum of the series η ΕΟ Σ ηχο – 1, 1x] <1. ΠΕ 1 (b) Find the sum of each of the following series. DO Σηχή, 1x <1 η = 1 η (i) Σ. (c) Find the sum of each of the following series. D) Σπίη – 1)x, Ix <1 ΠΕ 2 (i) Σ - η 57 ΠΕ 2 0 i) 22 = 1
(5) For n = 5, Verify the following summation formula: Σ + 1 (1) (η + 2)2"-1 10
Which is different than the others? O Σ2, (-1)+1 η 4η Ο Σ ! Ο Σ1 η 5n2 -5.7 6n2 -6.7 =1
We have a dataset with n = 10 pairs of observations (li, yi), and η Σ α: = 683, Σμι = 813, i=1 η i=1 η Σ? = 47, 405, Σαιξε = 56, 089, Συ - Συ? = 66, 731. i=1 What is an approximate 99% confidence interval for the mean response at xo = 90?