Understanding P Series and Related Concepts

What is a P series?

• A series that always diverges

• A series where the exponent is a variable

• A series with a constant exponent in the denominator

• A series that always converges

Under what condition does a P series converge?

• When p is between 0 and 1

• When p is less than 0

• When p equals 1

• When p is greater than 1

What is a harmonic series?

• A geometric series with a common ratio of 1

• A P series with p equal to 1

• A P series with p equal to 2

• A series that converges

How does a geometric series differ from a P series?

• In a P series, the exponent is a variable

• In a geometric series, the exponent is a variable

• In a geometric series, the base is a constant

• In a P series, the base is a constant

What is the value of p for the series 1/n^3?

• 1

• 3

• 1/3

• 0

If a series is 1/n^(1/2), what can be said about its convergence?

• It converges

• It diverges

• It is a geometric series

• It is not a P series

For the expression n^(2k - 5), what must be true for the series to converge?

• k = 0

• k > 3

• k < 3

• k = 3

In the expression n^(4k - 1), what condition must be met for convergence?

• k > 1/2

• k = 0

• k < 1/2

• k = 1/2

What does the nth term test determine?

• If a series converges when the limit is zero

• If a series diverges when the limit is zero

• If a series diverges when the limit is non-zero

• If a series converges when the limit is non-zero

What is the integral test used for?

• To find the sum of a series

• To determine if a series is geometric

• To determine the value of p in a P series

• To check if a series converges or diverges