Sequences and Series in Calculus
Math ⇒ Calculus
Sequences and Series in Calculus starts at 11 and continues till grade 12.
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See sample questions for grade 12
Determine whether the series ∑n=1∞ 1/(n(n+1)) converges or diverges.
Explain the difference between absolute convergence and conditional convergence of a series.
Find the sum of the first 10 terms of the arithmetic sequence 2, 5, 8, 11, ...
Find the sum of the first 5 terms of the geometric sequence 3, 6, 12, 24, ...
Given the series ∑n=1∞ 1/2n, find its sum.
If a sequence is monotonic and bounded, what can be said about its convergence?
If the nth term of a sequence is an = 3n - 2, what is the 5th term?
If the sequence an = (-1)n does not converge, what is the reason?
Which of the following is NOT a necessary condition for the convergence of a series?
(1) The terms must approach zero.
(2) The terms must be positive.
(3) The series must be infinite.
(4) The sequence of partial sums must be bounded.
Which of the following is the general term of the arithmetic sequence with first term 3 and common difference 5?
(1) an = 3n + 5
(2) an = 5n + 3
(3) an = 3 + 5(n-1)
(4) an = 5 + 3(n-1)
Which of the following series is convergent?
(1) ∑n=1∞ 1/n
(2) ∑n=1∞ 1/n2
(3) ∑n=1∞ n
(4) ∑n=1∞ (-1)n
Which of the following statements is true about the sequence an = (-1)n/n?
(1) It diverges.
(2) It converges to 0.
(3) It converges to 1.
(4) It oscillates without limit.
Fill in the blank: The limit of the sequence an = (2n+1)/(n+2) as n approaches infinity is _______.
Fill in the blank: The nth term of a geometric sequence with first term a and common ratio r is _______.
Fill in the blank: The sum of the first n terms of an arithmetic sequence is Sn = _______.
Fill in the blank: The sum to infinity of a geometric series with |r| < 1 is S = _______.
True or False: Every convergent sequence is bounded.
True or False: The alternating harmonic series ∑n=1∞ (-1)n+1/n converges.
True or False: The geometric series ∑n=0∞ arn converges if |r| < 1.
True or False: The sequence an = n/(n+1) converges to 1 as n approaches infinity.
