(2) Determine whether the following series converge. Rigorously justify your answers (using the convergence tests from the lecture). ∞ ∞ (a) Σ n 2n (b) n2+1 n! n=1 n=1 ∞ շո (c) Σ 1+2n n=0 (α) Σ ΣΣΣ (e) (-1)+1 +1 n=1 n=1 n! 1 (f) 3n+2' n=1 (2n)!*
(2) Determine whether the following series converge. Rigorously justify your answers (using the convergence tests from the lecture). ∞ ∞ (a) Σ n 2n (b) n2+1 n! n=1 n=1 ∞ շո (c) Σ 1+2n n=0 (α) Σ ΣΣΣ (e) (-1)+1 +1 n=1 n=1 n! 1 (f) 3n+2' n=1 (2n)!*
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+
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Question
Transcribed Image Text:(2) Determine whether the following series converge. Rigorously justify your answers
(using the convergence tests from the lecture).
∞
(a) Σ
n
2n
(b)
n2+1
n=1
n=1
n!
∞
(α) Σ
n=1
n²
n4
+1
(e) (-1)+1
n=1
1
∞
(©) Σ
շո
1+2n
n=0
∞
1
n!
(f)
3n+2'
n=1
(2n)!*
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