9. Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)
a) \(\sum_{n=0}^{\infty}\left(\frac{3 x}{5}\right)^{n}\)
b) \(\sum_{n=0}^{\infty} \frac{2^{n}(x-2)^{n}}{3 n}\)
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please answer all 9. Find the interval of convergence of the power series. (Be sure to include a check for conve...
Find the interval of convergence of the power series. (Be sure to include a check for...
Find the interval of convergence of the power series. (Be sure
to include a check for convergence at the endpoints of the
interval. If the answer is an interval, enter your answer using
interval notation. If the answer is a finite set of values, enter
your answers as a comma separated list of values.)
∞
n!(x + 9)n
1 · 3 · 5 ... (2n − 1)
n = 1
Find the interval of convergence of the power series. (Be sure to include a check for...
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation.) n!(x1 1 3.5 (2n 1) n 1
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of...
Find the interval of convergence of the power series. (Be sure to include a check for...
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation.) (-1)"+ (x - 2) 6
Find the interval of convergence of the power series. (Be sure to include a check for...
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation) (-1)(x - 3)”. 1 ng Submit Answer
Find the interval of convergence of the power series. (Be sure to include a check for...
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation.)
(1 point) Find the interval of convergence of the power series (x3)" l (n + 4)" Be sure to check ...
(1 point) Find the interval of convergence of the power series (x3)" l (n + 4)" Be sure to check the convergence at the endpoints of the interval and use round or square brackets as appropriate. The interval of convergence is: (1 point) Find the interval of convergence of the power series nt2x(-3)Y Be sure to check the convergence at the endpoints of the interval and use round or square brackets as appropriate. The interval of convergence is: (1 point)...
7. Use the Alternating Series Test to determine the convergence or divergence of the series
7. Use the Alternating Series Test to determine the convergence or divergence of the series a) \(\sum_{n=1}^{\infty} \frac{(-1)^{n} \sqrt{n}}{2 n+1}\)b) \(\sum_{n=1}^{\infty} \frac{(-1)^{n} n}{2 n-1}\)8. Use the Ratio Test or the Root Test to determine the convergence or divergence of the seriesa) \(\sum_{n=0}^{\infty}\left(\frac{4 n-1}{5 n+7}\right)^{n}\)b) \(\sum_{n=0}^{\infty} \frac{\pi^{n}}{n !}\)
find an expression for the area of the region under the graphf(x)=x^4 on the interval...
find an expression for the area of the region under the graph f(x)=x^4 on the interval [1,7]. use right-Hand endpoints as sample points choices1. area \(=\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(1+\frac{7 i}{n}\right)^{4} \frac{7}{n}\)2. area \(=\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(1+\frac{9 i}{n}\right)^{4} \frac{6}{n}\)3. area \(=\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(1+\frac{6 i}{n}\right)^{4} \frac{6}{n}\)4. area \(=\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(1+\frac{7 i}{n}\right)^{4} \frac{6}{n}\)5. area \(=\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(1+\frac{6 i}{n}\right)^{4} \frac{7}{n}\)6. area \(=\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(1+\frac{9 i}{n}\right)^{4} \frac{7}{n}\)
Use a power series to approximate the definite integral,
17 Use a power series to approximate the definite integral, \(I\), to six decimal places.$$ \int_{0}^{0.4} \frac{x^{5}}{1+x^{7}} d x $$Find the radius of convergence, \(R\), of the series.$$ \sum_{n=1}^{\infty} \frac{x^{n+4}}{4 n !} $$$$ R= $$Find the interval, \(I\), of convergence of the series. (Enter your answer using interval notation.) \(I=\)
Determine whether the series converges, and if so, find its sum.
Determine whether the series converges, and if so, find its sum. (1) \(\sum_{n=1}^{\infty} 3^{-n} 8^{n+1}\)\((2) \sum_{n=2}^{\infty} \frac{1}{n(n-1)}\)(3) \(\sum_{n=0}^{\infty}(-3)\left(\frac{2}{3}\right)^{2 n}\)(4) \(\sum_{n=1}^{\infty} \frac{1}{e^{2 n}}\)(5) \(\sum_{n=1}^{\infty} \ln \frac{n}{n+1}\)(6) \(\sum_{n=1}^{\infty}[\arctan (n+1)-\arctan n]\)(7) \(\sum_{n=1}^{\infty} \ln \left(\frac{n^{2}+4}{2 n^{2}+1}\right)\)(8) \(\sum_{n=1}^{\infty} \frac{1+2^{n}}{3^{n}}\)(9) \(\sum_{n=1}^{\infty}\left[\cos \frac{1}{n^{2}}-\cos \frac{1}{(n+1)^{2}}\right]\)
Find the interval of convergence of the power series. (Be sure
to include a check for convergence at the endpoints of the
interval. If the answer is an interval, enter your answer using
interval notation. If the answer is a finite set of values, enter
your answers as a comma separated list of values.)
∞
n!(x + 9)n
1 · 3 · 5 ... (2n − 1)
n = 1
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation.) n!(x1 1 3.5 (2n 1) n 1
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of...
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation.) (-1)"+ (x - 2) 6
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation) (-1)(x - 3)”. 1 ng Submit Answer
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation.)
(1 point) Find the interval of convergence of the power series (x3)" l (n + 4)" Be sure to check the convergence at the endpoints of the interval and use round or square brackets as appropriate. The interval of convergence is: (1 point) Find the interval of convergence of the power series nt2x(-3)Y Be sure to check the convergence at the endpoints of the interval and use round or square brackets as appropriate. The interval of convergence is: (1 point)...
17 Use a power series to approximate the definite integral, \(I\), to six decimal places.$$ \int_{0}^{0.4} \frac{x^{5}}{1+x^{7}} d x $$Find the radius of convergence, \(R\), of the series.$$ \sum_{n=1}^{\infty} \frac{x^{n+4}}{4 n !} $$$$ R= $$Find the interval, \(I\), of convergence of the series. (Enter your answer using interval notation.) \(I=\)
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