WOLFRAM NOTEBOOK

Leibniz Criterion for Alternating Series

​
n
20
zoom
An alternating series
∞
∑
n=1
n
(-1)
a
n
converges if
a
1
≥
a
2
≥…>0
and
lim
n∞
a
n
=0
. Even partial sums
S
2N
=
2N
∑
n=1
n
(-1)
a
n
form an increasing sequence and odd partial sums
S
2N-1
=
2N-1
∑
n=1
n
(-1)
a
n
form a decreasing sequence; their limit is the same.

External Links

Permanent Citation

Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.