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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

What is an effect on the convergence of a series if each term in an alternating series ∑n=1∞(−1)nan\sum_{n=1}^{\infty} (-1)^n a_n∑n=1∞​(−1)nan​ is replaced by ln⁡(n+1n)\ln\left(\frac{n+1}{n}\right)ln(nn+1​), assuming that all original terms were decreasing and positive?

Question 2
college-boardCalculus AB/BCAPExam Style
1 mark

What general guideline can be given regarding the first error bound when approximating the summation of an infinite series ∑n=1∞(−1)nan\sum_{n=1}^{\infty} (-1)^n a_n∑n=1∞​(−1)nan​ whose terms are increasing positive functions?

Question 3
college-boardCalculus AB/BCAPExam Style
1 mark

What is the error bound when using the third term of an alternating series ∑n=1∞(−1)n+13n2\sum_{n=1}^{\infty} (-1)^{n+1} \frac{3}{n^2}∑n=1∞​(−1)n+1n23​ to approximate its sum?

Question 4
college-boardCalculus AB/BCAPExam Style
1 mark

What is true about an alternating series with decreasing positive terms starting with a negative leading coefficient whose nth partial sum exceeds its limit by more than twice the (n+2)(n+2)(n+2)nd-term?

Question 5
college-boardCalculus AB/BCAPExam Style
1 mark

If the series (−1)n3n2(-1)^n \frac{3}{n^2}(−1)nn23​ converges, what is the maximum value of ∣s−sn∣|s - s_n|∣s−sn​∣ when using the Alternating Series Error Bound to approximate the sum sss with s8s_8s8​?

Question 6
college-boardCalculus AB/BCAPExam Style
1 mark

Which of the following best describes the relationship between the error bound and the accuracy of an approximation?

Question 7
college-boardCalculus AB/BCAPExam Style
1 mark

If the alternating series ∑n=1∞(−1)n+1n2\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^2}∑n=1∞​n2(−1)n+1​ has its error bound calculated using the first four terms, what is the maximum possible error?

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Question 8
college-boardCalculus AB/BCAPExam Style
1 mark

If the radial coordinate changes sign while the angular coordinate remains fixed, what happens to a point's location?

Question 9
college-boardCalculus AB/BCAPExam Style
1 mark

If an alternating series satisfies ∣an+1∣≤∣an∣|a_{n+1}| \leq |a_n|∣an+1​∣≤∣an​∣ for all nnn and lim⁡n→∞an=0\lim_{n \to \infty} a_n = 0limn→∞​an​=0, what can we say about using its nth term as an error estimate when approximating its sum?

Question 10
college-boardCalculus AB/BCAPExam Style
1 mark

If an alternating series ∑(−1)n−1an\sum (-1)^{n-1}a_n∑(−1)n−1an​ is convergent, and a10=0.005a_{10} = 0.005a10​=0.005, what is an upper bound for the error in using S9S_9S9​ to approximate the sum of the series?