(1) Suppose that Σ an converges and Σ bn diverges. Show that Σ (an +b.) diverges. (1) Suppose that Σ an converges and Σ bn diverges. Show that Σ (an +b.) diverges.
1. Decide if the following statements are true or false. Give an explanation for your answer. (a) If 0 < an < bn and Σ an converges, then Σ bn converges (b) If 0 < an < bn and Σ an diverges, then Σ bn diverges. (c) If bn an 0 andbcoverges, then an converges (d) If Σ an converges, then Σ|an| converges (e) If Σ an converges, then linn lan +1/a (f) Σχ00(-1)"cos(nn) is an alternating series (g) The...
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
6. (1 point) Prove that if (an+ba) diverges. bn diverges, then an converges and nel KSB: 0MFA CIN 8. (1 point) Find the total length of the zigzag path. Note that each bounce meets a side at a right angle and bounces off at a 30° angle. 30% L 6. (1 point) Prove that if (an+ba) diverges. bn diverges, then an converges and nel KSB: 0MFA CIN 8. (1 point) Find the total length of the zigzag path. Note that...
+00 bn are series with positive terms an and (a) Suppose that O bn is convergent. Prove that if "limo and that I1 n= 1 +00 then Σ an is also convergent. (b) Use part (a) to show that the series converges t In (n) +00 bn are series with positive terms an and (a) Suppose that O bn is convergent. Prove that if "limo and that I1 n= 1 +00 then Σ an is also convergent. (b) Use part...
(b) Determine whether the series Σ7n+= converges or diverges. n=1 Σ(-1)n+1n2+1 (c) Determine whether the series converges absolutely, con- n= 1 verges conditionally or diverges (d) Find the interval of convergence for the power series Σ(-1)k (2r)* k-2 (b) Determine whether the series Σ7n+= converges or diverges. n=1 Σ(-1)n+1n2+1 (c) Determine whether the series converges absolutely, con- n= 1 verges conditionally or diverges (d) Find the interval of convergence for the power series Σ(-1)k (2r)* k-2
Determine whether the following series converges absolutely, converges conditionally, or diverges. 00 (-1)+1e 3k Σ-11: -Σ ak (k 17 k 1 k 1 Find lim a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. koo O A. lim ak koo O B. The Ilimit does not exist. (1)* 1 (k 17) 3k e Σ. Now, let denote What can be concluded from this result using the Divergence Test? k 1 O...
1. Determine if each series converges absolutely, or conditionally (if any), or diverges. (c) Σ(V2-1) (a) Σ- 11n n Innn)n 1. Determine if each series converges absolutely, or conditionally (if any), or diverges. (c) Σ(V2-1) (a) Σ- 11n n Innn)n
Select all that are true. Determine if the sequence converges or diverges. If it converges, find the limit: bn = (Vn+2020 - Vn)((n +2021) * another answer converges to 0 diverges by the divergence criterion converges to 1010 converges to 2020 diverges converges to 1/2
Determine whether the following series converges or diverges (show your answer in detail). 00 k Σ k=3k + 2tan-k+2
bn converges 18. Let (an)n=1 and (bn)n=1 be sequences in R. Show that if and lan – an+1 < oo, then anbr converges.