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

Question 1
college-boardCalculus AB/BCAPExam Style
1 mark

For what values of ppp does the infinite series ∑n=1∞1(3n+2)p\sum_{n=1}^{\infty} \frac{1}{(3n+2)^p}∑n=1∞​(3n+2)p1​ converge according to the p-Series Test?

Question 2
college-boardCalculus AB/BCAPExam Style
1 mark

For the series ∑n=1∞1n2\sum_{n=1}^{\infty} \frac{1}{n^{2}}∑n=1∞​n21​ what is the p-value of the series?

Question 3
college-boardCalculus AB/BCAPExam Style
1 mark

Which of the following sums is representative of the harmonic series?

Question 4
college-boardCalculus AB/BCAPExam Style
1 mark

If the series ∑n=1∞1np\sum_{n=1}^{\infty} \frac{1}{n^p}∑n=1∞​np1​ is convergent for p>1p > 1p>1, what is the impact on convergence if ppp is replaced with (p−0.5)(p-0.5)(p−0.5) in this p-series?

Question 5
college-boardCalculus AB/BCAPExam Style
1 mark

Which series definitely diverges based on its form?

Question 6
college-boardCalculus AB/BCAPExam Style
1 mark

What is the relationship between a harmonic series and a p-series?

Question 7
college-boardCalculus AB/BCAPExam Style
1 mark

Given a p-series ∑n=1∞1np\sum_{n=1}^{\infty} \frac{1}{n^p}∑n=1∞​np1​, for which value of ppp will it be guaranteed to converge?

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Question 8
college-boardCalculus AB/BCAPExam Style
1 mark

How does replacing every term in the harmonic sequence ∑k=2∞(−1)kk\sum_{k=2}^{\infty} \frac{(-1)^k}{k}∑k=2∞​k(−1)k​ with their respective natural logarithms affect its convergence?

Question 9
college-boardCalculus AB/BCAPExam Style
1 mark

What conclusion can be drawn about the convergence of the series ∑n=2∞(−1)nln⁡(n)\sum_{n=2}^{\infty} \frac{(-1)^{n}}{\ln(n)}∑n=2∞​ln(n)(−1)n​ using alternating series tests?

Question 10
college-boardCalculus AB/BCAPExam Style
1 mark

If the series ∑n=1∞(−1)n+1n\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}∑n=1∞​n(−1)n+1​ is known to converge, what does this imply about the behavior of its sequence of partial sums?