Math Archive: Questions from 2024-03-23

Does the series ∑ n = 1 ∞ 1 n + 35 converge or diverge? Why? The series converges because its terms approach zero. The series diverges because it can be rewritten as ∑ n = 1 ∞ 1 n + 35 = ∑ n = 35 ∞ 1 n, which is the harmonic series and diverges. The series diverges because it can be rewritten as ∑ n = 1 ∞ 1 n + 35 = ∑ n = 36 ∞ 1 n, which is the harmonic series and diverges. The series diverges because its terms approach zero. The series converges because the limit of its sequence of partial sums is finite. The series diverges because the limit of its sequence of partial sums does not exist.

25-28 Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in Example 6). If it is convergent, find its sum. 25. ∑ n=2 ∞ 2 n 2 − 1 26. ∑ n = 1 ∞ ln ⁡ n n + 1 27. ∑ n = 1 ∞ 3 n(n + 3) 28. ∑ n=1 ∞ ( e 1/n − e 1/(n + 1))