∞ 00 Suppose an>0 and a diverges. Prove that n=1 n =. an contrary suppose Σ an p=g¹ + a₂ converges, then 1+ an an 1+ an diverges. (Hint: On the 1 ›0.) 1+1/an

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 6E
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∞
∞
Suppose an >0 and a diverges. Prove that
n = 1
n=1
∞
an
an
contrary suppose Σ
converges, then
I + An
1+ an
n=0
an
1+ an
diverges. (Hint: On the
1
>0.)
1+1/an
Transcribed Image Text:∞ ∞ Suppose an >0 and a diverges. Prove that n = 1 n=1 ∞ an an contrary suppose Σ converges, then I + An 1+ an n=0 an 1+ an diverges. (Hint: On the 1 >0.) 1+1/an
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