does this series converge or diverge? if converges enter the sum of the series. explain step by step

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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does this series converge or diverge? if converges enter the sum of the series. explain step by step 

Σ₁{In √n +1 − In √n}
in=
Transcribed Image Text:Σ₁{In √n +1 − In √n} in=
Expert Solution
Step 1

The given series can be expanded as

        (ln √2 - ln √1) + (ln √3 - ln √2) + (ln √4 - ln √3) + . . . . . . + ( ln √(n+1) - ln √n) + . . . . . . 

      = limn→∞  [ ln √(n+1) - ln √1 ]

      = limn→∞  [ ln √(n+1) - 0 ]

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