Question

2. Prove that the harmonic series $\sum_{n=1}^{\infty} 1/n$ is divergent by comparing it with the series $1 + \frac{1}{2} + (\frac{1}{4} + \frac{1}{4}) + (\frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8}) + (8 \text{ terms each equal to } \frac{1}{16}) + ...$, which is $1 + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + ...$

          2. Prove that the harmonic series $\sum_{n=1}^{\infty} 1/n$ is divergent by comparing it with the series
$1 + \frac{1}{2} + (\frac{1}{4} + \frac{1}{4}) + (\frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8}) + (8 \text{ terms each equal to } \frac{1}{16}) + ...$,
which is $1 + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + ...$

2. Prove that the harmonic series ∑n=1^∞ 1/n is divergent by comparing it with the series
1 + (1)/(2) + ((1)/(4) + (1)/(4)) + ((1)/(8) + (1)/(8) + (1)/(8) + (1)/(8)) + (8 terms each equal to (1)/(16)) + ...,
which is 1 + (1)/(2) + (1)/(2) + (1)/(2) + (1)/(2) + ...

Added by Mark W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Khoobchandra Agrawal

01/05/2022

Step 1

Step 1: We want to prove that the harmonic series \sum_(n=1)^(∞) (1)/(n) is divergent by comparing it with the series 1+(1)/(2)+(1)/(2)+(1)/(2)+(1)/(2)+cdots. Show more…

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Prove that the harmonic series sum_(n=1)^(infty ) (1)/(n) is divergent by comparing it with the series terms each equal to {(:(1)/(16))+cdots}, which is ,1+(1)/(2)+(1)/(2)+(1)/(2)+(1)/(2)+cdots. 2. Prove that the harmonic series En= 1/n is divergent by comparing it with the series 1 + 118 8 1 1 2 12 1- 8 terms each equal to 2 1 1 2 which is 1