Calculus - Series Projects

Test for convergence or divergence, absolute or conditional. If the series converges and it is possible

Problem: Test for convergence or divergence, absolute or conditional. If the series converges and it is possible to find the sum, then do so.

\[\sum\limits_{n=1}^{\infty }{\frac{3}{{{2}^{n}}}}\]

Problem: Test for convergence or divergence, absolute or conditional. If the series converges and it is possible to find the sum, then do so.

\[\sum\limits_{n=2}^{\infty }{\frac{1}{n\ln n}}\]

Problem: Test for convergence or divergence, absolute or conditional. If the series converges and it is possible to find the sum, then do so.

\[\sum\limits_{n=0}^{\infty }{\frac{3{{n}^{2}}+n+1}{{{n}^{4}}+1}}\]

Problem: Test for convergence or divergence, absolute or conditional. If the series converges and it is possible to find the sum, then do so.

\[\sum\limits_{n=1}^{\infty }{\frac{n+1}{2n+3}}\]

Problem: Test for convergence or divergence, absolute or conditional. If the series converges and it is possible to find the sum, then do so.

\[\sum\limits_{n=1}^{\infty }{\frac{n!}{{{2}^{n}}{{n}^{2}}}}\]

Problem: Test for convergence or divergence, absolute or conditional. If the series converges and it is possible to find the sum, then do so.

\[\sum\limits_{n=1}^{\infty }{\frac{{{(-1)}^{n}}}{\sqrt{n}}}\]

Problem: Find the open interval of convergence, and test the endpoints for absolute and conditional convergence.

\[\sum\limits_{n=1}^{\infty }{\frac{{{(x+1)}^{n}}}{{{3}^{n}}n}}\]

Problem: Find the open interval of convergence, and test the endpoints for absolute and conditional convergence.

\[\sum\limits_{n=1}^{\infty }{\frac{{{(x-4)}^{n+1}}}{{{(n+3)}^{2}}}}\]

Problem: Find the Maclaurin series in closed form:

\[f(x)=\frac{1}{{{(x+1)}^{2}}}\]

Problem: Find the Maclaurin series in closed form of:

\[f(x)=\ln ({{x}^{2}}+1)\]

Problem: Find the critical points and test for relative extrema:

\[f(x,y)=2{{x}^{2}}+2xy+{{y}^{2}}+2x-3\]

Problem: Maximize:

\[f(x,y)=\sqrt{6-{{x}^{2}}-{{y}^{2}}}\]

Constraint

\[x+y-2=0\]

Price: $16.18

Solution: The downloadable solution consists of 11 pages, 518 words.
Deliverable: Word Document