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The Alternating Series, Ratio, and Root Tests- HW Problems
Determine if the following series converge or diverge.
(−1) 𝑛
1. ∑∞
𝑛=1 √𝑛
[cos(𝑛+1)𝜋][𝑛]
2. ∑∞
𝑛=1
𝑛2+1
𝑛
∞ (−1) (2𝑛−1)
3. ∑𝑛=1
3𝑛+1
(−1)𝑛
4. Show that ∑∞
𝑛=1 converges and determine how many terms
𝑛5
of the sum are necessary so that the absolute value of the error
between the partial sum and the entire sum is less than 0.0001.
5. Approximate the sum so that the absolute value of the error is less
than 0.0001.
(−1) 𝑛
𝑎. ∑∞
𝑛=1 𝑛!
(−1)𝑛
𝑏. ∑∞
𝑛=1 4
(𝑛+1)
The Alternating Series, Ratio, and Root Tests- HW Problems
Determine if the following series converge or diverge.
(−1) 𝑛
1. ∑∞
𝑛=1 √𝑛
[cos(𝑛+1)𝜋][𝑛]
2. ∑∞
𝑛=1
𝑛2+1
𝑛
∞ (−1) (2𝑛−1)
3. ∑𝑛=1
3𝑛+1
(−1)𝑛
4. Show that ∑∞
𝑛=1 converges and determine how many terms
𝑛5
of the sum are necessary so that the absolute value of the error
between the partial sum and the entire sum is less than 0.0001.
5. Approximate the sum so that the absolute value of the error is less
than 0.0001.
(−1) 𝑛
𝑎. ∑∞
𝑛=1 𝑛!
(−1)𝑛
𝑏. ∑∞
𝑛=1 4
(𝑛+1)
