Why does the alternating harmonic series, with terms (minus 1) to the n over n, converge?

• Its magnitudes decrease to zero
• Its terms are all positive
• Its partial sums are bounded by 1
• The ratio test gives a limit of 0

Why does the alternating harmonic series converge?

• Its magnitudes decrease to zero
• Its terms are all positive
• The ratio test gives a limit of 0

Stopping an alternating series after 10 terms leaves error at most the 11th magnitude.

Circle one:   True   False

Terms minus 1 to the n over n squared converge absolutely. Type p of the absolute p-series.

Answer: ______________

An alternating series has decreasing magnitudes. A partial sum through 4 terms omits from term 5 on. Type the error bound as a multiple of the 5th magnitude.

Answer: ______________

Approximating the alternating harmonic series with its first 10 terms leaves an error of at most what?

• 1/11
• 1/10
• 1/100
• 0

Which series converges, but its absolute version diverges?

• sum (minus 1) to the n over n
• sum 1 over n squared
• sum (1/2) to the n
• sum n over 2 to the n

Which series converges, but its absolute version diverges?

• sum 1 over n squared
• sum minus 1 to the n over n
• sum 1 over 2 to the n

Ten terms of the alternating harmonic series leave an error of at most what?

• 1 over 11
• 1 over 10
• 1 over 100

A student says the alternating harmonic series converges, so the plain harmonic series must converge too. What is the error?

• The alternating test also proves the harmonic series converges
• Removing the signs can break convergence; that gap is conditional convergence
• The harmonic terms do not tend to zero