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WorksheetsQuiz on Applied Mathematics II set by walle T.
Total questions: 10
Worksheet time: 5mins
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
