CALCULUS II TEST 3 REVIEW EXAM SOLVED #18
How to solve for Interval of Convergence - correct answer Conduct a Ratio Test and
solve for the center and the radius. Once found, use the center and the radius in the
formula |(x - c)| < R. After that, find the upper and lower values. Then, plug the upper
and lower values into the original series' equation to determine whether the function
converges/diverges. (Remember: convergence uses brackets when using interval
notation, and divergence uses parentheses when using interval notation.)
What does a Geometric Series look like? - correct answer ar^n, and S = a / (1 - r)
Does the harmonic series converge or diverge? - correct answer The harmonic series --
DIVERGES.
Does the alternating harmonic series converge or diverge? - correct answer The
alternating harmonic series -- CONVERGES.
What does the Taylor Series formula look like? - correct answer The sum from n = 1 to
infinity of...
([f^(n) (c)] * (x-c)^n) / n!
Where...
F^n = f, f prime, f double prime, etc.
C = the center
N = the number of terms
Sorry! This is confusing. F^n just means the number of times the derivative was taken.
Also, it's supposed to be f(c), but it doesnt look like it.
Riemann's Rearrangement Theorem - correct answer If an INFINITE SERIES is
CONDITIONALLY CONVERGENT, then ITS TERMS can be REARRANGED so that
the new series CONVERGES to ANY GIVEN VALUE or so that it DIVERGES.
How to test if a series is convergent or divergent? - correct answer Root/Ratio tests
determine ABSOLUTE CONVERGENCE.
Nth term test determines DIVERGENCE.
Every other test determines CONDITIONAL CONVERGENCE.
What does a telescoping series look like? - correct answer The sum from n = 0 to infinity
of
(b1 - b2) + (b2 - b3) + (b3 - b4)...
What do you do for the Direct Comparison Test? - correct answer Pull out the n and
eveything touching the n, then use the guidelines from the test i.e. An converges if
0=<an<=bn and bn converges
How to solve for Interval of Convergence - correct answer Conduct a Ratio Test and
solve for the center and the radius. Once found, use the center and the radius in the
formula |(x - c)| < R. After that, find the upper and lower values. Then, plug the upper
and lower values into the original series' equation to determine whether the function
converges/diverges. (Remember: convergence uses brackets when using interval
notation, and divergence uses parentheses when using interval notation.)
What does a Geometric Series look like? - correct answer ar^n, and S = a / (1 - r)
Does the harmonic series converge or diverge? - correct answer The harmonic series --
DIVERGES.
Does the alternating harmonic series converge or diverge? - correct answer The
alternating harmonic series -- CONVERGES.
What does the Taylor Series formula look like? - correct answer The sum from n = 1 to
infinity of...
([f^(n) (c)] * (x-c)^n) / n!
Where...
F^n = f, f prime, f double prime, etc.
C = the center
N = the number of terms
Sorry! This is confusing. F^n just means the number of times the derivative was taken.
Also, it's supposed to be f(c), but it doesnt look like it.
Riemann's Rearrangement Theorem - correct answer If an INFINITE SERIES is
CONDITIONALLY CONVERGENT, then ITS TERMS can be REARRANGED so that
the new series CONVERGES to ANY GIVEN VALUE or so that it DIVERGES.
How to test if a series is convergent or divergent? - correct answer Root/Ratio tests
determine ABSOLUTE CONVERGENCE.
Nth term test determines DIVERGENCE.
Every other test determines CONDITIONAL CONVERGENCE.
What does a telescoping series look like? - correct answer The sum from n = 0 to infinity
of
(b1 - b2) + (b2 - b3) + (b3 - b4)...
What do you do for the Direct Comparison Test? - correct answer Pull out the n and
eveything touching the n, then use the guidelines from the test i.e. An converges if
0=<an<=bn and bn converges
