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8.4. ALTERNATING SERIES
Activity 8.21.
For (a)-(j), use appropriate tests to determine the convergence or divergence of the
following series. Throughout, if a series is a convergent geometric series, find its sum.
(a)
∞
k=3
2
√
k − 2
(b)
∞
k=1
k
1 + 2k
(c)
∞
k=0
2k 2 + 1
k 3 + k + 1
(d)
∞
k=0
100 k
k!
(e)
∞
k=1
2 k
5 k
(f)
∞
k=1
k 3 − 1
k 5 + 1
(g)
∞
k=2
3 k−1
7 k
(h)
∞
k=2
1
k k
(i)
∞
k=1
(−1) k+1
√
k + 1
(j)
∞
k=2
1
k ln(k)
(k) Determine a value of n so that the nth partial sum S n of the alternating series
∞
n=2
(−1) n
ln(n)
approximates the sum to within 0.001.
⊳
8.4. ALTERNATING SERIES
Activity 8.21.
For (a)-(j), use appropriate tests to determine the convergence or divergence of the
following series. Throughout, if a series is a convergent geometric series, find its sum.
(a)
∞
k=3
2
√
k − 2
(b)
∞
k=1
k
1 + 2k
(c)
∞
k=0
2k 2 + 1
k 3 + k + 1
(d)
∞
k=0
100 k
k!
(e)
∞
k=1
2 k
5 k
(f)
∞
k=1
k 3 − 1
k 5 + 1
(g)
∞
k=2
3 k−1
7 k
(h)
∞
k=2
1
k k
(i)
∞
k=1
(−1) k+1
√
k + 1
(j)
∞
k=2
1
k ln(k)
(k) Determine a value of n so that the nth partial sum S n of the alternating series
∞
n=2
(−1) n
ln(n)
approximates the sum to within 0.001.
⊳