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2. Prove whether 8 (-1)+1 j √j²+1 j=1 converges absolutely, converges conditionally, or diverges.

2. Prove whether 8 (-1)+1 j √j²+1 j=1 converges absolutely, converges conditionally, or diverges.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 25E
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Real Analysis II: Solve the problem in photo 1 following notes in photo 2
{a} 09. AST. I fant in numbers and Defi Eaj ex. 2.0 Conv. by A-S-T ex. |a₁ ≤ ( 8 W. &a fact a lim an o is abs Conv. abs. Conv.. because J+1 Study 3/5 = 1/2 1/² "1 is E B₁Aj every Eaj decreasing seg of positive then & (-1)+ NOT Thim: (Absolute Convergence Test) If Assume If Eaj Conv. abs, then 2(a) Conv. Eaj Conv. abs. [Since |aj| = |aj| t; = 1, ... j we Ɛaj get Eaj Conv. 80 if 2 lail Conv... yes abs. Conv. an Converges- Conv. (P-Sehes p=2 X EA CON. (Harmonic, Siv) Problem Bj Elajh Conv. aux Coution the Converse is false Def if Eaj Conv. but does not Conv. abs then Eag Convergo Condition 22 either diverges Conv. abs, от Conv. Conditi EGI A = 1 = 1/2 + 1/3 - 1/14 + 1/5 - 1/6 + 1/ 7- / 8 + 1/ 7- / 10 + 1/11 - 1/12 + 1/3 - 1/12/ #½-1⁄2-1⁄4-16-18-1/10 - 1/12 - 1/14
Transcribed Image Text:{a} 09. AST. I fant in numbers and Defi Eaj ex. 2.0 Conv. by A-S-T ex. |a₁ ≤ ( 8 W. &a fact a lim an o is abs Conv. abs. Conv.. because J+1 Study 3/5 = 1/2 1/² "1 is E B₁Aj every Eaj decreasing seg of positive then & (-1)+ NOT Thim: (Absolute Convergence Test) If Assume If Eaj Conv. abs, then 2(a) Conv. Eaj Conv. abs. [Since |aj| = |aj| t; = 1, ... j we Ɛaj get Eaj Conv. 80 if 2 lail Conv... yes abs. Conv. an Converges- Conv. (P-Sehes p=2 X EA CON. (Harmonic, Siv) Problem Bj Elajh Conv. aux Coution the Converse is false Def if Eaj Conv. but does not Conv. abs then Eag Convergo Condition 22 either diverges Conv. abs, от Conv. Conditi EGI A = 1 = 1/2 + 1/3 - 1/14 + 1/5 - 1/6 + 1/ 7- / 8 + 1/ 7- / 10 + 1/11 - 1/12 + 1/3 - 1/12/ #½-1⁄2-1⁄4-16-18-1/10 - 1/12 - 1/14
2. Prove whether 8 (-1)+1 j √j²+1 j=1 converges absolutely, converges conditionally, or diverges.
Transcribed Image Text:2. Prove whether 8 (-1)+1 j √j²+1 j=1 converges absolutely, converges conditionally, or diverges.
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