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 ±∞ ∑n−1n2−1

Question

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 ±∞  ∑n−1n2−1

coffentw · Accepted Answer

The objective here is to determine whether the given series is convergent, diverges to ±∞, or diverges, not to ±∞ Series is: ∑n−1n2−1 First simplify the nth term of the series as: an=n−1n2−1=n−1(n−1)(n+1)=1n+1 ∑n−1n2−1=∑1n+1, and 1n&amp;lt;1n+1 and ∑1n is convergent by p-test series Thus, by comparison test series ∑1n+1=∑n−1n2−1 is convergent. And it diverges to ∞ since the series ∑1n diverges to ∞ Thus, the given series diverges to ∞

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

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}

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Answer & Explanation

New Questions in Calculus 2