This Series Has
Mood Swings
Mood Swings
This is what happens to the series
\sum_{k=1}^{\infty}\frac{(-1)^k}{k}
What is convergence?
This phrase describes the behavior of \sum_{k=1}^{\infty}\frac{(-1)^k}{k}
What is conditional convergence?
This test is best for \sum\_{k=1}^{\infty}\frac{1}{k^{2/3}}
What is p- series test?
This is the type of series that describes \sum_{k=0}^{\infty}x^k
What is a power series?
This is the radius of convergence of \sum_{k=0}^{\infty}x^k
What is 1?
This is why the alternating series \sum_{k=1}^{\infty}\frac{(-1)^k}{\sqrtk} converges.
What is "the terms go to zero"?
This describes the convergence of \sum_{k=1}^{\infty}\frac{(-1)^k}{k^2}
What is absolute?
This test is best for
\sum_{k=1}^{\infty}\frac{3^k}{4^k}
What is geometric series test?
This is the center of the series
\sum_{k=0}^{\infty}a_k(x-3)^k
What is 3?
This is the radius of convergence for \sum_{k=0}^{\infty}kx^k
What is 1?
This is what happens to \sum\_{k=1}^{\infty}(-1)^k\frac{k}{k+1} .
What is divergence?
This describes the behavior of \sum\_{k=1}^{\infty}\frac{(-1)^k}{\sqrt{k^2+1}
What is conditional convergence?
This convergence test is best for \sum\_{k=1}^{\infty}\frac{k+4}{5^k}
What is ratio test?
This is the type of series that describes \sum_{k=1}^{\infty}\frac{1}{k^2}
This is the radius of convergence of \sum_{k=0}^{\infty}\frac{x^k}{k!}
What is infinity?
This is the first thing you must check for when using the Alternating Series Test.
What is "the limit of
b_k goes to 0"?
This is the type of convergence for this series \sum\_{k=1}^{\infty}(-1)^k\frac{k}{k^0.9}
What is divergence?
This test is best for \sum\_{k=1}^{\infty}\frac{k+1}{k^3+k}
What is comparison/limit comparison test?
This is the center of the series \sum\_{k=2}^{\infty}(3x-2)^k
What is
\frac{2}{3}?
This is the center and radius of
\sum_{k=0}^{\infty}\frac{(x-2)^k}{k}
What is center 2 and radius 1?
This is what happens to \sum\_{k=2}^{\infty}\frac{(-1)^k}{k^2-1} .
What is convergence?
This type of convergence applies to \sum\_{k=1}^{\infty}(-1)^{k+1}\frac{10^k}{k!}
What is absolute convergence?
This test is best for
\sum_{k=1}^{\infty}\frac{7^{k+2}}{(k+3)!}.
What is ratio test?
This is the center of the series
\sum_{k=0}^{\infty}\frac{(-1)^k(4k-1)}{4^k(k!)}x^k
What is 0?
This is the radius of convergence for
\sum_{k=0}^{\infty}\frac{(x+1)^k}{2^k}
What is 2?