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  2. AP Calculus
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Infinite Sequences and Series (BC Only)

Question 1
college-boardCalculus AB/BCAPExam Style
1 mark

What is the sum of the convergent p-series ∑n=1∞1np\sum_{n=1}^{\infty} \frac{1}{n^p}∑n=1∞​np1​ when p>1p>1p>1?

Question 2
college-boardCalculus AB/BCAPExam Style
1 mark

Which test can be used to determine whether the infinite series ∑n=2∞(−1)nn\sum_{n=2}^{\infty} \frac{(-1)^n}{\sqrt{n}}∑n=2∞​n​(−1)n​ converges or diverges?

Question 3
college-boardCalculus AB/BCAPExam Style
1 mark

Which series can be used to test whether the series for f(x)=x1+xf(x)=\frac{x}{1+x}f(x)=1+xx​ converges or diverges around x=5x=5x=5?

Question 4
college-boardCalculus AB/BCAPExam Style
1 mark

What is the sum of the infinite series ∑n=4∞(−1n(2n)(ln⁡n))\sum_{n=4}^{\infty}\left(\frac{-1^{n}}{(2^n)(\ln{n})}\right)∑n=4∞​((2n)(lnn)−1n​) given that it alternates in sign and decreases in absolute value?

Question 5
college-boardCalculus AB/BCAPExam Style
1 mark

What is the value of the infinite series ∑n=1∞1n2\sum_{n=1}^{\infty} \frac{1}{n^2}∑n=1∞​n21​?

Question 6
college-boardCalculus AB/BCAPExam Style
1 mark

What must be true for a function represented by an alternating harmonic series ∑(−1)n+1f(n)n\sum (-1)^{n+1} \frac{f(n)}{n}∑(−1)n+1nf(n)​ to converge if lim⁡n→∞f(n)\lim_{n \to \infty} f(n)limn→∞​f(n) exists?

Question 7
college-boardCalculus AB/BCAPExam Style
1 mark

Which test is commonly used to determine the convergence of a harmonic series, ∑n=1∞1n\sum_{n=1}^{\infty} \frac{1}{n}∑n=1∞​n1​?

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Question 8
college-boardCalculus AB/BCAPExam Style
1 mark

What is the sum of the series ∑n=2∞(−1)nln⁡(n)\sum_{n=2}^{\infty} \frac{(-1)^n}{\ln(n)}∑n=2∞​ln(n)(−1)n​?

Question 9
college-boardCalculus AB/BCAPExam Style
1 mark

Which of the following series is a p-series with p-value of 1/2?

Question 10
college-boardCalculus AB/BCAPExam Style
1 mark

If a civil engineer determines that the force exerted by wind on a skyscraper can be modeled as a p-series with p=2.5p = 2.5p=2.5, what is the implication for the total force when all floors (from ground floor to infinity) are considered?