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mathematics
precalculus

Questions and Answers of Precalculus

Find the radius of convergence and interval of convergence of the series.
Find the radius of convergence and interval of convergence of the series.
Find the radius of convergence and interval of convergence of the series. Σn"χ" 'x' n-
Find the radius of convergence and interval of convergence of the series. (-1)"x" Σ n? n-1
Find the radius of convergence and interval of convergence of the series. (-1)"x" п. п-1 п
Test the series for convergence or divergence. Σ (-1) η-1
Test the series for convergence or divergence.
Test the series for convergence or divergence.
Test the series for convergence or divergence. 1 Σ п n=1 _n'+1/n
Test the series for convergence or divergence. Σ n=1 n + n cos?n 2. n cosʻn
Test the series for convergence or divergence. n2 Σ п п+1 п—1
Test the series for convergence or divergence. (п!)" п*" п31
Test the series for convergence or divergence. 5* Σ 3k + 4* k=1
Test the series for convergence or divergence. ο Σ (-1)- j+ 5 j=1
Test the series for convergence or divergence.
Test the series for convergence or divergence. 1/п el/n ,2 n° п-1 п
Test the series for convergence or divergence. k In k (k + 1)3 k=1 ÎM:
Test the series for convergence or divergence.
Test the series for convergence or divergence. п! 2. п—1 еn?
Test the series for convergence or divergence. En sin(1/n) n=1
Test the series for convergence or divergence. E tan(1/n) n=1
Test the series for convergence or divergence. k-1 2 + sin k
Test the series for convergence or divergence.
Test the series for convergence or divergence. Vk - 1 Σ 00 (/k + 1) k=1 k
Test the series for convergence or divergence. In n ο0 Σ (-1) Vη η-1
Test the series for convergence or divergence.
Test the series for convergence or divergence. 1:3: 5 Σ (2п — 1) (Зп — 1) 2·5· 8 ·
Test the series for convergence or divergence. Vn* + 1 00 3 п? + п n=1
Test the series for convergence or divergence. 2k-13k+1 00 k* k=1 ÎM:
Test the series for convergence or divergence.
Test the series for convergence or divergence.
Test the series for convergence or divergence. ο0 Σ /k? + 1 k=1 k
Test the series for convergence or divergence.
Test the series for convergence or divergence. Σnen ,3 n=1
Test the series for convergence or divergence.
Test the series for convergence or divergence.
Test the series for convergence or divergence. Σ n=2 n/In n
Test the series for convergence or divergence. n2n Σ (1 + п)эп 00 Зп п31 И
Test the series for convergence or divergence.
Test the series for convergence or divergence.
Test the series for convergence or divergence. n2 – 1 Σ(-1). n' + 1 .3 n=1
Test the series for convergence or divergence. 00 п — 1 п-1 п° + 1
Test the series for convergence or divergence. ² – 1 п? Σ п-1 п + 1
For which positive integers k is the following series convergent? (п!)? (kn)! п-1
Let {bn} be a sequence of positive numbers that converges to 1/2. Determine whether the given series is absolutely convergent. 00 (-1)"n! Σ . .. bn n"b,b2b3 n=1
A series o an is defined by the equationsa1 = 1Determine whether o an converges or diverges. 2 + cos n ал an+1
Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent.
Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent.
Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent. sin(nT/6) Σ 1 + n/n 00 N. n=1
Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent. п п Σ In n п32
Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent. n52n n+1 n=1
Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent. (-9)" Σ n=1 n10"+1
Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent. п Σ 2 + 3n n=1
Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent.
Use the Root Test to determine whether the series is convergent or divergent.
Use the Root Test to determine whether the series is convergent or divergent. ,2 п 00 Σ п п%31
Use the Root Test to determine whether the series is convergent or divergent. 5n -2n Σ n + 1 n=1
Use the Root Test to determine whether the series is convergent or divergent. (-1)"-1 Σ (In n)" 00 n=2
Use the Root Test to determine whether the series is convergent or divergent. (-2)" п" п-1
Use the Root Test to determine whether the series is convergent or divergent. п 00 n² + 1 Σ 2n2 + 1 п-1
Use the Ratio Test to determine whether the series is convergent or divergent. 2" n! Σ (-1)"- 5· 8: 11 • ... ·(3n + 2) n=1 8.
Use the Ratio Test to determine whether the series is convergent or divergent. 2·4·6·...· (2n) 2·4·6 · n! n=1 8.
Use the Ratio Test to determine whether the series is convergent or divergent. 2·5· 8· 11 2: 5 2:5· 8 + .. 3· 5 3·5·7 3·5·7·9
Use the Ratio Test to determine whether the series is convergent or divergent.
Use the Ratio Test to determine whether the series is convergent or divergent. (2п)! (п!)? п-1
Use the Ratio Test to determine whether the series is convergent or divergent.
Use the Ratio Test to determine whether the series is convergent or divergent.
Use the Ratio Test to determine whether the series is convergent or divergent. cos(nп/3) п! п31
Use the Ratio Test to determine whether the series is convergent or divergent.
Use the Ratio Test to determine whether the series is convergent or divergent. 00 пт" Σ (-3)"-1 п31
Use the Ratio Test to determine whether the series is convergent or divergent.
Use the Ratio Test to determine whether the series is convergent or divergent.
Use the Ratio Test to determine whether the series is convergent or divergent. 00 Σ kek k=1
Use the Ratio Test to determine whether the series is convergent or divergent. k=i k! K!
Use the Ratio Test to determine whether the series is convergent or divergent.
Use the Ratio Test to determine whether the series is convergent or divergent. 00 3" n-1 3 2"n3 n=1
Use the Ratio Test to determine whether the series is convergent or divergent.
Use the Ratio Test to determine whether the series is convergent or divergent.
Determine whether the series is absolutely convergent or conditionally convergent. Σ (-1)-1, n2 + 4 п п-1
Determine whether the series is absolutely convergent or conditionally convergent.
Determine whether the series is absolutely convergent or conditionally convergent.
Determine whether the series is absolutely convergent or conditionally convergent.
Determine whether the series is absolutely convergent or conditionally convergent. (-1)*-1 Σ 00 In л—1
For what values of p is each series convergent? (In n)" Σ (-1)" η-2 п
For what values of p is each series convergent?
Approximate the sum of the series correct to four decimal places. (-1)"-1 п 4" п-1
Approximate the sum of the series correct to four decimal places.
Approximate the sum of the series correct to four decimal places. n+1 Σ ,6 п п31
Approximate the sum of the series correct to four decimal places.
Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy? (| error | < 0.00005) Σ n-1 п
Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy?
Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy?
Graph both the sequence of terms and the sequence of partial sums on the same screen. Use the graph to make a rough estimate of the sum of the series. Then use the Alternating Series Estimation
Graph both the sequence of terms and the sequence of partial sums on the same screen. Use the graph to make a rough estimate of the sum of the series. Then use the Alternating Series Estimation
Test the series for convergence or divergence. 00 E (-1)*(/n + 1 – n) n-1
Test the series for convergence or divergence.
Test the series for convergence or divergence.
Test the series for convergence or divergence.
Test the series for convergence or divergence.
Test the series for convergence or divergence. sin(n + )7 1 + yn TT п-0

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