Questions from General Calculus


Q: If ∑ an is a convergent series with positive terms, is

If ∑ an is a convergent series with positive terms, is it true that ∑ sin (an) is also convergent?

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Q: Graph the first several partial sums sn(x) of the

Graph the first several partial sums sn(x) of the series∑∞n=0xn, together with the sum function f (x)= 1/ (1 – x), on a common screen. On what interval do these partial sums appear to be converging to...

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Q: Find all positive values of b for which the series ∑∞n

Find all positive values of b for which the series ∑∞n=1 b ln n converges.

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Q: Show that if an > 0 and limn→∞ nan ≠ 0

Show that if an > 0 and limn→∞ nan ≠ 0 then ∑an is divergent.

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Q: Find all values of c for which the following series converges.

Find all values of c for which the following series converges.

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Q: If the nth partial sum of a series ∑∞n-1

If the nth partial sum of a series ∑∞n-1 an is sn = n - / n + 1 find an and ∑∞n-1 an.

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Q: If the nth partial sum of a series ∑∞n-1

If the nth partial sum of a series ∑∞n-1 an is sn = 3 – n2-n, find an and ∑∞n-1 an.

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Q: Determine whether the sequence is increasing, decreasing, or not monotonic

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

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Q: Determine whether the sequence is increasing, decreasing, or not monotonic

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

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Q: Determine whether the sequence is increasing, decreasing, or not monotonic

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

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