Calculus 2: Sequences and Series

42 videos • 7,856 views • by Math Problems Solved Craig Faulhaber
1
Find the limit of a_n = (4n+1)! / (4n-1)! as n goes to infinity (Sequences 1)
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2
Find the limit of 1/n^3 + 2^2/n^3 + 3^2/n^3 +...+n^2/n^3 as n goes to infinity (Sequences 2)
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3
Find the limit as n goes to infinity of a_n= ln((7n-7)/(3n+4)) (Sequences #3)
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4
Find the form of the nth term of the sequence 1/2 , 2/5, 3/10, 4/17, 5/26, 6/37, ... (Sequences #4)
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5
Determine whether the following series converges or diverges: SUM n/sqrt(n^2+13) (Series 1)
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6
Determine whether the following converges or diverges a_n=7n/(3-4n). SUM(7n/(3-4n)) (Series 2)
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7
Use the integral test to determine whether the series converges or diverges (Series 3)
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8
Use the integral test to determine if SUM ( 1 / (n^2 + 36) ) is convergent or divergent (Series 4)
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9
Use the integral test to determine whether the series is convergent SUM n^2/(n^3+3)^(3/2) (Series 5)
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10
Determine whether SUM 2ne^(-n^2) converges using the integral test (Series 6)
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11
Compute the 5th partial sum S_5. Estimate the error. Find a better estimate of the sum (Series 7)
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12
Compute the improper integral and determine whether the series converges int 7x^2e^(-x^3) (Series 8)
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13
Determine whether the series SUM_1^infty 7/(2+3^n) converges or diverges. (Series #9)
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14
Determine whether the infinite series SUM{ n/sqrt(n^8+1) } converges or diverges (Series #10)
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15
Use the Direct Comparison Test on each of the following series... (Series 11)
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16
Use the Limit Comparison Test to determine whether the series converges or diverges (Series 12)
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17
Do the following series converge or diverge? 5 rapid-fire problems!
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18
Determine wheether the series SUM (-1)^n sin(1/n) and SUM (-1)^n cos(1/n) converges or diverges.
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19
Does the series SUM (-1)^(n+1)/(7n^2+3) converge. Does it converge absolutely?
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20
Does the series SUM ( cos(n*pi)/n(3/5) ) converge conditionally, converge absolutely or diverge?
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21
How many terms of the series do we need to add to find the sum to the desired accuracy? (-1)^n / n^2
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22
Apply the ratio test to determine the convergence of the series. SUM{(n!)^2/(2n)!}
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23
Consider the series SUM 10^n/[(n+1)4^(2n+1)]. Evaluate L. What does the Ratio Test say about...
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24
Convergent or Divergent Series 20
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25
Convergent or Divergent Series 21
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26
Convergent or Divergent Series 22. Another root test problem.
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27
Interval of Convergence 1
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28
Interval of Convergence 2
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29
Interval of Convergence 3
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30
Interval of Convergence 4 (Ratio Test)
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31
Interval of Convergence 5 (Ratio Test)
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32
Interval of Convergence 6 (Root Test!)
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33
Interval of Convergence 7 (Ratio Test Example!)
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34
Find the Power Series representation of f(x)=ln(1-x^2)
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35
MacLaurin Series 1: Write out the first four terms of the Maclaurin series of f(x)
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36
MacLaurin Series 2: By recognizing each series below as a Taylor series evaluated at a particular va
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37
Taylor Series 3: Write the Taylor series for f(x)=x^3 about x=1 as ∑_(n=0)^∞ c_n (x−1)^n
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38
Limit Comparison with SUM ln(n)/n^3 (Convergent or Divergent Series 23)
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39
Write the Taylor series for f(x)=sin⁡x about x=π/2. Find the first 5 coefficients.
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40
For which values of p will the series converge?
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41
Write the Taylor series for f(x)=e^x about x=1. Find the first 5 coefficients.
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42
Find the first 4 nonzero terms of the Taylor Series for f(x)=4/x centered at x=-2
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