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SECONDARY
CALCULUS AND ANALYSIS
CALCULUS 2
SERIES
Secondary
Calculus and Analysis
Precalculus
Calculus 1
Calculus 2
Series
Differential equations
Applications of integrals
Parametric equations, polar coordinates, and vector-valued functions
Algebra
Geometry
Statistics and Probability
Math Word Problem
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Recent Series Answers
Series
asked 2021-03-18
Find the radius of convergence, R, of the series.
\(\sum_{n=1}^\infty\frac{(2x+9)^n}{n^2}\)
Find the interval, I, of convergence of the series.
Series
asked 2021-03-18
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.
\(\sum_{n=1}^\infty\frac{n^2}{(n+1)(n^2+2)}\)
Series
asked 2021-03-12
Determine whether the series
\(\sum a_n\)
an converges or diverges: Use the Alternating Series Test.
\(\sum_{n=2}^\infty(-1)^n\frac{n}{\ln(n)}\)
Series
asked 2021-03-11
Find the radius of convergence and interval of convergence of the series.
\(\sum_{n=1}^\infty\frac{x^n}{n5^n}\)
Series
asked 2021-03-11
Determine if the following series converges or diverges. If it is a converging geometric or telescoping series, or ca be written as one, provide what the series converges to.
\(\displaystyle{\sum_{{{k}={2}}}^{\infty}}{\frac{{{k}}}{{{k}^{{3}}-{17}}}}\)
Series
asked 2021-03-11
Taylor series and interval of convergence
a. Use the definition of a Taylor/Maclaurin series to find the first four nonzero terms of the Taylor series for the given function centered at a.
b. Write the power series using summation notation.
c. Determine the interval of convergence of the series.
\(f(x)=\log_3(x+1),a=0\)
Series
asked 2021-03-11
Determine the first four terms of the Maclaurin series for sin 2x
(a) by using the definition of Maclaurin series.
(b) by replacing x by 2x in the series for sin 2x.
(c) by multiplying 2 by the series for sin x by the series for cos x, because sin 2x = 2 sin x cos x
Series
asked 2021-03-09
Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for ƒ (perhaps more than once). Give the interval of convergence for the resulting series.
\(g(x)=-\frac{1}{(1+x)^2}\text{ using }f(x)=\frac{1}{1+x}\)
Series
asked 2021-03-08
Determine the radius and interval of convergence for each of the following power series.
\(\sum_{n=0}^\infty\frac{2^n(x-3)^n}{\sqrt{n+3}}\)
Series
asked 2021-03-08
Use the Limit Comparison Test to determine the convergence or divergence of the series.
\(\sum_{n=1}^\infty\frac{2n^2-1}{3n^5+2n+1}\)
Series
asked 2021-03-08
Write out the first few terms of each series to show how the series start. Then find out the sum of the series.
\(\sum_{n=0}^\infty(\frac{5}{2^n}+\frac{1}{3^n})\)
Series
asked 2021-03-07
Consider the series
\(\sum_{n=1}^\infty\frac{(-1)^n}{n^2}\)
a) Show the series converges or diverges using the alternating series test.
b) Approximate the sum using the 4-th partial sum(
\(S_4\)
) of the series.
c) Calculate the maximum error between partial sum(
\(S_4\)
) and the sum of the series using the remainder term portion of the alternating series test.
Series
asked 2021-03-07
Use the binomial series to find the Maclaurin series for the function
\(f(x)=\sqrt{1+x^3}\)
Series
asked 2021-03-07
Determine the radius of convergence and the interval of convergence for each power series.
\(\sum_{n=0}^\infty\sqrt{n}(x-1)^n\)
Series
asked 2021-03-07
Determine whether the series converges or diverges.
\(\displaystyle{\sum_{{{n}={2}}}^{\infty}}{\frac{{{1}}}{{{n}{\ln{{n}}}}}}\)
Series
asked 2021-03-07
Use the Root Test to determine the convergence or divergence of the series.
\(\sum_{n=1}^\infty(\frac{n}{500})^n\)
Series
asked 2021-03-06
Consider the following series.
\(\sum_{n=1}^\infty\frac{\sqrt{n}+4}{n^2}\)
The series is equivalent to the sum of two p-series. Find the value of p for each series.
Determine whether the series is convergent or divergent.
Series
asked 2021-03-06
Find the interval of convergence of the power series.
\(\sum_{n=0}^\infty\frac{x^{5n}}{n!}\)
Series
asked 2021-03-06
Verify that the infinite series converges.
\(\displaystyle{\sum_{{{n}={0}}}^{\infty}}{\left(-{0.2}\right)}^{{n}}={1}-{0.2}+{0.04}-{0.008}+\ldots\)
Series
ANSWERED
asked 2021-03-05
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.
\(\sum_{n=1}^\infty\frac{(2n)!}{n^5}\)
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