Quiz on Applied Mathematics II set by walle T.

What is the definition of a sequence?

• A function whose domain is the collection of all positive integers

• A function whose domain is the collection of all integers greater than or equal to a given integer

• A function whose domain is the collection of all real numbers

• A function whose domain is the collection of all negative integers

When does a sequence converge?

• When the terms of the sequence become very close to a fixed number

• When the terms of the sequence increase continuously

• When the terms of the sequence become negative

• When the terms of the sequence are all equal

What is the sum of the series ∑∞n=1 (1/2)^n?

• 2

• 3/2

• 1/2

• 1

When does a series diverge?

• When the sum of the series is a real number

• When the sequence of partial sums is convergent

• When the sum of the series exists

• When the sequence of partial sums is divergent

What is the nth partial sum of a Telescopic series?

• bn + bn+1

• b1 - bn

• bn - bn+1

• bn - bn-1

What is the nth partial sum of a telescopic series given by ∑∞n=1(bn−bn+1)?

• bn−bn+1

• bn

• 1

• bn+1

When does a geometric series converge?

• r ≤ -1

• -1 < r < 1

• r ≥ 1

• r = 0

What convergence test is most effective for series involving factorials or powers?

• Integral Test

• Comparison Test

• Root Test

• Ratio Test

What is the limit of n√(n/(5n)) as n approaches infinity?

• 0

• ∞

• 2

• 1

For which value of r does the series ∑∞n=1(n!/(2^n)) diverge?

• r = ∞

• r = 2

• r = 1

• r = 0