Series
Author: Chris Rosenthal
Date: July 21, 2010

 \sum_{n = 1}^{k }  \frac{ 1 }{n } 

\sum_{n = 1 }^{k }  \frac {1} {n^2}

 \sum_{n = 1 }^{k } ( \frac{ 1 }{2 } )^n

 \sum_{n = 1 }^{k } 1^n

 \sum_{n = 1 }^{k }  (-1) ^{n+1}

Slide k to see if each series converges or diverges.

 \sum_{n=1 }^{k }  \frac{ (-1)^{n+1} }{n } 

k = 1 (slider from 1 to 100, step 1)
a = Sum(Sequence[1.0 / n, n, 1.0, k])
A: (1.0, a)
b = Sum(Sequence[1.0 / n^(2.0), n, 1.0, k])
B: (2.0, b)
c = Sum(Sequence[0.5^(n), n, 1.0, k])
C: (3.0, c)
d = Sum(Sequence[1.0^(n), n, 1.0, k])
D: (4.0, d)
e = Sum(Sequence[(-1.0)^(n + 1.0), n, 1.0, k])
E: (5.0, e)
f = Sum(Sequence[(-1.0)^(n + 1.0) / n, n, 1.0, k])
F: (6.0, f)