For each of the following series, using no tests besides the nth Term and Comparison Tests, determine whether the series converges, diverges to pminfty, or diverges, not to pminfty sumfrac{n-1}{n^2-1}

slaggingV 2020-10-26 Answered
For each of the following series, using no tests besides the nth Term and Comparison Tests, determine whether the series converges, diverges to ±, or diverges, not to ±
n1n21
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Expert Answer

coffentw
Answered 2020-10-27 Author has 103 answers

The objective here is to determine whether the given series is convergent, diverges to ±, or diverges, not to ±
Series is:
n1n21
First simplify the nth term of the series as:
an=n1n21=n1(n1)(n+1)=1n+1
n1n21=1n+1, and
1n<1n+1 and
1n is convergent by p-test series
Thus, by comparison test series
1n+1=n1n21 is convergent.
And it diverges to since the series 1n diverges to
Thus, the given series diverges to

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Jeffrey Jordon
Answered 2021-12-17 Author has 2047 answers

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